Table of contents

Imitating nature's mechanisms offers enormous potential for the improvement of our lives and the tools we use. This field of the study and imitation of, and inspiration from, nature's methods, designs and processes is known as biomimetics. Artificial muscles, i.e. electroactive polymers (EAPs), are one of the emerging technologies enabling biomimetics. Polymers that can be stimulated to change shape or size have been known for many years. The activation mechanisms of such polymers include electrical, chemical, pneumatic, optical and magnetic. Electrical excitation is one of the most attractive stimulators able to produce elastic deformation in polymers. The convenience and practicality of electrical stimulation and the continual improvement in capabilities make EAP materials some of the most attractive among activatable polymers (Bar-Cohen Y (ed) 2004 Electroactive Polymer (EAP) Actuators as Artificial Muscles—Reality, Potential and Challenges 2nd edn, vol PM136 (Bellingham, WA: SPIE Press) pp 1–765). As polymers, EAP materials offer many appealing characteristics that include low weight, fracture tolerance and pliability. Furthermore, they can be configured into almost any conceivable shape and their properties can be tailored to suit a broad range of requirements. These capabilities and the significant change of shape or size under electrical stimulation while being able to endure many cycles of actuation are inspiring many potential possibilities for EAP materials among engineers and scientists in many different disciplines. Practitioners in biomimetics are particularly excited about these materials since they can be used to mimic the movements of animals and insects. Potentially, mechanisms actuated by EAPs will enable engineers to create devices previously imaginable only in science fiction.

For many years EAP materials received relatively little attention due to their poor actuation capability and the small number of available materials. In the last fifteen years, a series of new materials have emerged that exhibit large displacement in response to electrical stimulation. This capability is making them highly attractive as actuators for their operational similarity to biological muscles, particularly their resilience, quiet operation, damage tolerance and ability to induce large actuation strains (stretching, contracting or bending). The application of these materials as actuators involves multi-disciplines including materials, electromechanics, chemistry, computers and electronics. Even though the force of actuation of existing EAP materials and their robustness requires further improvement, there has already been a series of reported successes in the development of EAP-actuated mechanisms. Using EAP to replace existing actuators may be a difficult challenge and therefore it is highly desirable to identify a niche application where EAP materials would not need to compete with existing technologies.

EAP materials can be divided into two major groups based on their activation mechanism: ionic or electronic. Electronic EAPs, such as electrostrictive, electrostatic, piezoelectric and ferroelectric, are driven by Coulomb forces. These types of EAP material can be made to hold the induced displacement while activated under a DC voltage, allowing them to be considered for robotic applications. These materials have high mechanical energy density and they can be operated in air with no major constraints. However, electronic EAPs require high activation fields (>10 V/μm) that are close to the breakdown level. In contrast to electronic EAPs, ionic EAPs are materials that involve the transport of ions and they consist of two electrodes and an electrolyte. The activation of ionic EAPs can be achieved by voltages as low as 1–2 volts. Examples of ionic EAPs include gels, polymer–metal composites, conducting polymers and carbon nanotubes. Their disadvantages are a need to maintain wetness and their low electromechanical coupling.

Turning EAP materials into actuators-of-choice requires a well established infrastructure. This involves improving the understanding of the basic principles that drive the various EAP materials. It is also necessary to develop a comprehensive material science, as well as effective electro-mechanics analytical tools and material processing techniques. Efforts are underway to study the parameters that control EAP electro-activation force and deformation and many successes have been reported. The processes of synthesizing, fabricating, electroding, shaping and handling are being refined to maximize the actuation capability and robustness of EAP materials. Methods of reliably characterizing the response of these materials are being developed and efforts are being made to establish a database with documented material properties in order to support design engineers who are considering the use of these materials.

Grand challenge for the development of EAP-actuated robotics.

The technology of artificial muscles is still in its emerging stages but the increased resources, growing number of investigators conducting research related to EAP, and improved collaboration among developers, users and sponsors are leading to rapid advances in this field. In 1999, in an effort to promote worldwide development towards the realization of the potential of EAP materials, Yoseph Bar-Cohen posed an arm-wrestling challenge (http://ndeaa.jpl.nasa.gov/nasa-nde/lommas/eap/EAP-armwrestling.htm). A graphic rendering of this challenge is illustrated in the above figure. In posing this challenge, he is seeking to see an EAP-activated robotic arm win against a human in a wrestling match in order to provide a gauge of the level of advances in the development of these materials. Success in wrestling against humans will enable capabilities that are currently considered impossible. It would allow applying EAP materials to improve many aspects of our life where some of the possibilities include effective implants and prosthetics, active clothing and realistic biologically inspired robots, as well as fabricating products with unmatched capabilities and dexterity. The first arm-wrestling match against a human (a 17 year-old female high school student) was held on 7 March 2005 as part of the EAP-in-Action session of SPIE's EAPAD conference. Three robotic arms participated in the contest and the girl won against all these arms. Subsequent contests are now focusing on measuring the performance of the robotic arms compared to the student performance that was recorded in the 2006 contest. In a future conference, once advances in developing such arms reach a sufficiently high level, a professional wrestler will be invited for the next human/machine wrestling match.

This issue of the journal is dedicated to publishing recent research advances in the field of EAPs and is the first such dedicated issue ever to be published. The included papers cover the whole spectrum of elements considered critical to the development of the EAP technology infrastructure. The issue ends with a paper from the research group at EMPA describing their work on one of the first three arms that participated in the first historical arm-wrestling match. In the coming year the editors are hoping to see a significant growth in the amount of research and related publications addressing the many challenges that this field still poses.

In this paper, a dynamic model of a simply supported ionic polymer–metal composite (IPMC) beam resting on human tissue is developed. First, the bending moment in the IPMC beam due to the alternative electric potential is derived from Nemat-Nasser's hybrid actuation model. This explicit bending moment expression provides an easy way to estimate the bending capacity of the IPMC. Subsequently, the bending moment expression is incorporated in the analytical solution of beam transverse vibration to describe the response of the IPMC beam to an electric potential. The pressure generated by the IPMC beam on human tissue is then estimated by numerical integration. Comparisons show that the results obtained are comparable with the experimental data in the literature. Finally, to achieve the maximum deflection and total pressure, the optimal electrode length and location are discussed. To increase the flexibility and variety of beam deformation, multiple electrodes are considered. The deflection curve and generative pressure for multiple electrodes are also derived. The developed model is useful not only for biomedical devices that employ IPMC materials but also for any other applications that utilize the vibration of IPMC materials.

Plants have the ability to move fluids using the chemical energy available with bio-fuels. The energy released by the cleavage of a terminal phosphate ion during the hydrolysis of a bio-fuel assists the transport of ions and fluids in cellular homeostasis. The device discussed in this paper uses protein pumps cultured from plant cells to move fluid across a membrane barrier for controllable fluid transport. This paper demonstrates the ability to reconstitute a protein pump extracted from a plant cell on a supported bilayer lipid membrane (BLM) and use the pump to transport fluid expending adenosine triphoshate (ATP). The AtSUT4 protein used in this demonstration is cultured from Arabidopsis thaliana. This protein transporter moves a proton and a sucrose molecule in the presence of an applied proton gradient or by using the energy released from adenosine triphosphate's hydrolysis reaction. The BLM supporting the AtSUT4 is formed from 1-Palmitoyl-2-Oleoyl-sn-Glycero-3-[Phospho-L-Serine] (sodium salt) (POPS), 1-Palmitoyl-2-Oleoyl-sn-Glycero-3-Phosphoethanolamine (POPE) lipids supported on a porous lead silicate glass plate. The BLM is formed with the transporter and the ATP-phosphohydrolase (red beet ATPase) enzyme, and the ATP required for the reaction is added as a magnesium salt on one side of the membrane. The ATP hydrolysis reaction provides the required energy for transporting a proton–sucrose molecule through the protein pump. It is observed that there is no fluid transport in the absence of the enzyme and the amount of fluid transported through the membrane is dependent on the amount of enzyme reconstituted in the BLM for a fixed sucrose concentration. This demonstrates the dependence of the fluid flux on the ATP hydrolysis reaction catalyzed by the ATP-ase enzyme. The dependence of fluid flux on the amount of ATP-ase provides convincing evidence that the biochemical reaction is producing the fluid transport. The fluid flux resulting from the ATP-powered transport is observed to be higher than the rates observed with a proton concentration gradient driven transport reported in our earlier work.

A perfluorinated carboxylic acid membrane, i.e. Flemion, shows improved performance as actuator material compared with Nafion (perfluorinated sulfonic acid). Flemion has a higher ion exchange capacity and good mechanical strength. In particular, Flemion will deform with no back relaxation under applied electrical stimulus. However, with water as solvent, the operation of Flemion in air has serious problems, since water would evaporate quickly in air. Moreover, the electrochemical stability for use in water is around 1 V at room temperature. In previous work, investigations on Nafion with ionic liquid as solvents have been carried out by some researchers and good results have been obtained. In this work, we explore the use of highly stable ionic liquid instead of water as solvent in Flemion. Experimental results indicate that Flemion-based actuators with ionic liquid as solvent have improved stability as compared to the water samples. Although the forces exhibited by Flemion-based actuators with the use of ionic liquid decreased dramatically compared to water, these preliminary results suggest good potential for the use of Flemion with ionic liquid in future applications.

The numerous possible applications of ionic polymer–metal composites (IPMCs) as an underwater propulsor have led to the investigation of IPMC behaviour in an aqueous environment. This study compares the performance of an IPMC subjected to fluid drag forces to its performance without such forces. Both the form (i.e. pressure) drag and the viscous (i.e. skin friction) drag forces experienced by the IPMC due to the surrounding liquid are modelled. These forces are incorporated into a two-dimensional (2D) analytical model of a segmented IPMC. The model is based on small deflection and can be conveniently used. The maximum IPMC deflection for aqueous and non-aqueous environments is compared, both analytically and experimentally. Using video-capturing techniques, the deflection of the IPMC, both in air and in water, is investigated. The experimental results are used in order to better understand the performance of an IPMC in water. A large-deflection model for the segmented IPMC is also proposed.

Dielectric elastomer actuators (DEA) have been studied extensively under laboratory conditions where they have shown promising performance. However, in practical applications, they have not achieved their full potential. Here, the results of detailed analytical and experimental studies of the failure modes and performance boundaries of DEAs are codified into design principles for these actuators. Analysis shows that the performance of DEAs made with highly viscoelastic polymer films is governed by four key mechanisms: pull-in failure, dielectric strength failure, viscoelasticity and current leakage. Design maps showing the effect of these four mechanisms on performance under varying working conditions are proposed. This study shows that the viscous nature of DEA is very important in their performance/reliability trade-offs. A proper balance of performance and reliability is key to successful design of DEAs.

This paper reports the fabrication of a dry-type conducting polymer actuator using nitrile rubber (NBR) as the base material in a solid polymer electrolyte. The conducting polymer, poly(3,4-ethylenedioxythiophene) (PEDOT), was synthesized on the surface of the NBR layer by using a chemical oxidation polymerization technique. Room-temperature ionic liquids (RTIL) based on imidazolium salts, e.g. 1-butyl-3-methyl imidazolium X (where X = BF₄⁻, PF₆⁻, (CF₃SO₂)₂N⁻), were absorbed into the composite film. The compatibility between the ionic liquids and the NBR polymer was confirmed by DMA. The effect of the anion size of the ionic liquids on the displacement of the actuator was examined. The displacement increased with increasing anion size of the ionic liquids. The cyclic voltammetry responses and the redox switching dynamics of the actuators were examined in different ionic liquids.

We report on actuation in high tensile strength yarns of twist-spun multi-wall carbon nanotubes. Actuation in response to voltage ramps and potentiostatic pulses is studied to quantify the dependence of the actuation strain on the applied voltage. Strains of up to 0.5% are obtained in response to applied potentials of 2.5 V. The dependence of strain on applied voltage and charge is found to be quadratic, in agreement with previous results on the actuation of single-wall carbon nanotubes, with the magnitude of strain also being very similar. The specific capacitance reaches 26 F g⁻¹. The modulus of the yarns was found to be independent of applied load and voltage within experimental uncertainty.

The electrochemomechanical deformation (ECMD) of conducting polymers can be used to create soft actuators or transducers for the conversion of electric power to mechanical work. Polypyrrole (PPy) films, which were electrodeposited from a methyl benzoate solution of tetrabutylammonium (TBA) trifluoromethansulfonate, TBACF₃SO₃, were used to investigate the energy conversion efficiency. The films are known to have high tensile strength and to produce large strain at high stress in ECMD. The current as a function of load stress under constant applied potentials versus a reference electrode was studied in various electrolytes. Reduction currents increased with increasing load stress for contraction of the film (lifting weights) as well as for the oxidation current (expansion), indicating that the electrical input was sensing the load hung on the actuators. During the contraction, the conversion efficiency was estimated from the mechanical work energy. The maximum work energy-per-cycle was 140 kJ m⁻³. It has been found that the energy conversion efficiencies are very small (<0.25%). Most of the input electrical energy is stored electrochemically, but a significant fraction is also dissipated.

Ionomeric polymer transducers have received considerable attention in the past several years. These actuators, sometimes referred to as artificial muscles, have the ability to generate large bending strain and moderate stress at low applied voltages. As sensors, ionic polymer transducers generate an electric response due to mechanical strain. Typically, ionic polymer transducers are composed of Nafion-117 membranes with platinum electrodes and are saturated with water diluents. Recently the authors have developed a novel fabrication technique called the direct assembly process (DAP), which allowed improved control of the electrode morphology and composition. The DAP consists of spraying two high surface area metal–ionomer electrodes on a Nafion membrane. The benefits of the DAP process over previous methods is the ability to control the thickness of the electrode, the ability to control the composition of the electrode layer of the transducer, and the ability for it to be used with a wide variety of diluents. In past work we have demonstrated that platinum, ruthenium dioxide, and single-walled carbon nanotubes can be used as electrode material with diluents such as water, formamide, and ionic liquids. In this work we will present a reliability study of transducers fabricated using the DAP. Water-hydrated transducers dehydrate and stop moving within 5 min while operating in air under the application of ± 2 V. Ionic liquid based transducers are demonstrated to operate in air for over 400 000 cycles with little loss in performance, and are reliable up to 1 million cycles with a performance loss of less than 43%. The main source of degradation is the adhesion of the conductive surface to the high surface area electrode. This is enhanced in this study by using a PUU linking polymer that has good adhesion properties to gold. Large voltage and large strain are proven to decrease the life of the transducer. Formamide based samples are stable for 3 days under a 1 V actuation signal, while they are only reliable for 3–4 h under a 2 V actuation signal. Solvent evaporation is the main reason for degradation in formamide samples and it is increased at 2 V, indicating some electrochemical activity at such high voltages. Finally the initial drop in performance and the fluctuation in the generated strain are shown to be due to the loss of humidity absorbed from ambient air and the fluctuation in this ambient humidity, respectively.

Compact sensing methods are desirable for ionic polymer–metal composite (IPMC) actuators in microrobotic and biomedical applications. In this paper a novel sensing scheme for IPMC actuators is proposed by bonding an IPMC and a PVDF (polyvinylidene fluoride) thin film with an insulating layer in between. The insulating layer thickness is properly designed to minimize the stiffness of the composite IPMC/PVDF structure while reducing the electrical feedthrough coupling between the IPMC and PVDF. A distributed circuit model is developed to effectively represent the electrical coupling dynamics, which is then used in real-time compensation for extraction of the true sensing signal. Experimental results show that the developed IPMC/PVDF structure, together with the compensation algorithm, can perform effective, simultaneous actuation and sensing. As the first application, this sensori-actuator has been successfully used for performing and monitoring open-loop micro-injection of living Drosophila embryos.

An elastomeric but electrically conducting material is presented that is fabricated using a method inspired by ionic polymer–metal composites. The Young's modulus is only 10 MPa, and yet the conductivity is nearly 1 S cm⁻¹ and the material remains electrically conductive under uniaxial strains of 30%. Furthermore, this electrode material is photopatternable. Fabrication begins with mixing the platinum salt tetraammineplatinum(II) chloride into a UV-curable acrylated urethane elastomer precursor (Loctite 3108). The mixture is crosslinked under UV light in less than a minute and can therefore be patterned if it is exposed through a mask. The salt is then chemically reduced with sodium borohydride, which results in the formation of 100 nm sized platinum nodules on the surface of the film.

Mechanical prestrain is generally required for most electroelastomers to obtain high electromechanical strain and high elastic energy density. However, prestrain can cause several serious problems, including a large performance gap between the active materials and packaged actuators, instability at interfaces between the elastomer and prestrain-supporting structure, and stress relaxation. Difunctional and trifunctional liquid additives were introduced into 400% biaxially prestrained acrylic films and subsequently cured to form the second elastomeric network. The goal of this research was to determine the effect of different functional additives and concentrations on the microstructure, the mechanical properties, and the actuation of composite films. In the as-obtained interpenetrating polymer networks (IPNs), the additive network can effectively support the prestrain of the acrylic films and as a result, eliminate the external prestrain-supporting structure. However, the large amount of additive used to completely preserve prestrain was found to make the films too stiff, causing damage to IPN composite films. Furthermore, the interpenetrating network formed from a trifunctional monomer is more effective than that formed from a difunctional monomer in supporting the high tension of the VHB network. This high efficiency trifunctional additive leads to the enhancement of the breakdown field, due to less damage on the microstructure. The IPN composite films without external prestrain exhibit electrically-induced strains up to 300% in area, comparable to those of VHB 4910 films under high prestrain conditions.

In this paper, a new material, called a synthetic elastomer, is presented as a means of actuation. The material displays enhanced performances in terms of electrical as well as mechanical aspects such as dielectric constant, elastic strength and stress relaxation. We begin by developing synthesis procedures for the material, which result in its general recipe with chemical composition. In addition, the effects of respective chemical constituents are studied with regard to the electrical and mechanical characteristics of the actuator. Finally, experimental tests are performed to evaluate the actuation performance of the material, and its advantages are clarified by conducting comparative studies with other existing materials.

A bi-layer structure comprising a thin gold layer and a polypyrrole (PPy) film is developed as a valve. To create such structures, the thin metal layer is used as a working electrode, and the polypyrrole film is electrochemically deposited on the metal electrode. A layer of Cr deposited under a stationary part of the bi-layer flap adheres strongly to the gold layer and anchors the hinge of the flap, while the layer of polyimide deposited under a movable part of the flap adheres weakly to the gold layer of the flap. This bi-layer flap structure functions as an actuator valve for the opening and closing of an aperture. The actuation mechanism of the valve is based on a volume change in the PPy layer as cations move in and out of the polymer film during reduction and oxidation reactions. A bias of 1.2 V is used to actuate the flap. A method is proposed to increase the drug release system's functionality by placing the drug release flap within a protective enclosure that also serves as a drug reservoir. This integrated protection ensures reliable operation of the drug release flap unencumbered by surrounding tissues when used in vivo. A prototype system using a PDMS drug reservoir has been successfully tested in PBS buffer solution. The proposed integrated protection system holds promise for implantable biomedical devices.

Polymer-based linear actuators with contractile ability are currently demanded for several types of applications. Within the class of dielectric elastomer actuators, two basic configurations are available today for such a purpose: the multi-layer stack and the helical structure. The first consists of several layers of elementary planar actuators stacked in series mechanically and parallel electrically. The second configuration relies on a couple of helical compliant electrodes alternated with a couple of helical dielectrics. The fabrication of both these configurations presents some specific drawbacks today, arising from the peculiarity of each structure. Accordingly, the availability of simpler solutions may boost the short-term use of contractile actuators in practical applications. For this purpose, a new configuration is here described. It consists of a monolithic structure made of an electroded sheet, which is folded up and compacted. The resulting device is functionally equivalent to a multi-layer stack with interdigitated electrodes. However, with respect to a stack the new configuration is advantageously not discontinuous and can be manufactured in one single phase, avoiding layer-by-layer multi-step procedures. The development and preliminary testing of prototype samples of this new actuator made of a silicone elastomer are presented here.

The first arm wrestling match between a human arm and a robotic arm driven by electroactive polymers (EAP) was held at the EAPAD conference in 2005. The primary objective was to demonstrate the potential of the EAP actuator technology for applications in the field of robotics and bioengineering. The Swiss Federal Laboratories for Materials Testing and Research (Empa) was one of the three organizations participating in this competition. The robot presented by Empa was driven by a system of rolled dielectric elastomer (DE) actuators. Based on the calculated stress condition in the rolled actuator, a low number of pre-strained DE film wrappings were found to be preferential for achieving the best actuator performance. Because of the limited space inside the robot body, more than 250 rolled actuators with small diameters were arranged in two groups according to the human agonist–antagonist muscle configuration in order to achieve an arm-like bidirectional rotation movement. The robot was powered by a computer-controlled high voltage amplifier. The rotary motion of the arm was activated and deactivated electrically by corresponding actuator groups. The entire development process of the robot is presented in this paper where the design of the DE actuators is of primary interest. Although the robot lost the arm wrestling contest against the human opponent, the DE actuators have demonstrated very promising performance as artificial muscles. The scientific knowledge gained during the development process of the robot has pointed out the challenges to be addressed for future improvement in the performance of rolled dielectric elastomer actuators.

Five types of epoxy gels have been synthesized from common epoxy resins and hardeners. Fumed silica and nanoclay, respectively, were used as fillers and butyl methacrylate/acrylamide were used as monomer(s) for making interpenetrating polymer networks (IPNs) in three compositions. Swelling study, tensile property evaluation, dynamic mechanical thermal analysis, thermo-gravimetric analysis, scanning electron microscopy and electroactive property evaluation were done. The gels have sufficient mechanical strength and the time taken for bending to 20° was found to be 22 min for forward bias whereas it was just 12 min for reverse bias.

Based on femtosecond transient absorption spectroscopy, the charge carrier dynamics of CdS_xSe_1−x nanocrystal doped glasses was investigated by analyzing the nonlinear differential transient absorption spectra. Time constants were extracted, which are different from the literature results using similar samples: they are pump laser intensity-dependent and decrease with increasing pump laser intensity, whereas risetime constants are pump laser intensity-independent and high-order exciton recombination can be identified from the spectra. The threshold pump intensity was determined, which is lower than the literature result. Reasons for high-order recombination were analyzed, and broad size, state distribution and high pump intensity are found as key factors. Auger recombination may play a key role in the multi-exciton recombination. Theoretical calculations and analysis support this conclusion. A schematic model for electron transport and the formation of triexcitons in our samples are proposed to explain these results.

Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of the investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example. For the sake of completeness, the first part of the paper forms an introduction to wave propagation studies for damage detection. The local interaction simulation approach is implemented. This is followed by a series of two-dimensional studies of wave interaction with damage.

Wave propagation modelling is important for reliable damage detection based on Lamb waves. A number of different numerical computational techniques have been developed for wave propagation studies. The local interaction simulation approach, used for modelling sharp interfaces and discontinuities in complex media, has been applied effectively for numerical simulations of elastic wave interaction with structural damage. The paper builds upon this experience and reports numerical investigations of Lamb wave propagation modelling for damage detection in metallic structures. The ultimate objective of these investigations is to demonstrate that numerical simulations can significantly ease the monitoring strategy used for damage detection with Lamb waves. The interaction of fundamental Lamb wave modes with a rectangular damage slot in an aluminium plate is investigated as an example.

The second part of the wave propagation studies focuses on the monitoring strategy for damage detection. The effect of sensor position on the amplitude and time of flight of Lamb waves is investigated and discussed for various severities of damage. The results are validated experimentally.

The present work considers the possibility of vibration control of a distributed dynamical system, such as flexible plates using local piezoelectric (PZT) actuators/sensors and the electromechanical admittance concept. When PZT actuators bonded on structures are used in active vibration and acoustic control, the desired deformation field in the structure is obtained through the application of localized line forces and moments generated by applying an appropriate electrical field on the outer surfaces of the PZT patches. The electromechanical admittance generated at the electrical terminals of a PZT-driven smart structure is then extracted to synthesize a desired damping performance. This is achieved by a FEM-based minimization of the difference between the computed and the desired electromechanical admittance signature for investigated frequency ranges.

In this paper, a three-layered electro-magneto-elastic strip is investigated under a plane stress condition using finite element procedures. Two types of thermal loading, uniform temperature rise and non-uniform temperature distribution, are used. A two-dimensional rectangular element with four nodal degrees of freedom viz. thermal displacements in the x₁ and x₃ directions, and electric and magnetic potentials, is used to discretize the finite element model. The uncoupled and coupled analysis is carried out for two types of stacking sequence (B/F/B and F/B/F) under fixed–fixed and fixed–simply supported boundary conditions. Steady-state analysis is carried out to study the influence of piezo and magnetic constants on displacement, electric and magnetic potential across the thickness direction. It is found that the discontinuities of normal stress σ₁ occur on interfaces of two dissimilar materials across the thickness direction.

In this article we derive an analytical mathematical model for a micromachined silicon tuning-fork gyroscope which responds to an external angular rate by a rotation about its sensitive axis. The mechanical stress caused by the sense motion is detected with a piezoresistive read-out structure. Based on the mathematical model of a cantilevered beam with cubic crystal structure undergoing a coupled motion of bending and torsion, steady-state solutions for the mechanical stress components within the piezoresistive read-out structure are provided. The analytical results are compared with finite-element simulations and experimentally verified for a certain design of the read-out structure sensitive to shear stress. Providing fully analytical solutions of the mechanical stress distributions, this paper establishes a basis for optimizing the design of the read-out structure as well as its position and orientation of the angular rate sensor for maximum sensitivity.

A velocity feedback control system is evaluated in the active control of vibrations of a smart beam with a pair of surface mounted piezoelectric ceramic patches, and finite element (FE) model results are validated against measured ones. To this end, a three-layered smart beam FE model is utilized, where a partial layerwise theory and a fully coupled electro-mechanical theory are considered for the formulation of the displacement field and electric potential, respectively. Regarding the test rig, it consists of a cantilever smart aluminum beam with two piezoelectric patches mounted close to the clamped end. One of the piezoelectric patches is utilized to excite the beam while the other is utilized as an actuator in the feedback control loop. The control voltage applied to the actuator is proportional to the transverse velocity at the free end, which is measured by a laser vibrometer. First, the quasi-static actuation capacity of the piezoelectric patches is evaluated. Next, the free and forced velocity responses to an initial displacement field and harmonic excitation are analyzed. The capacity to predict instabilities and the accuracy of the FE model are demonstrated and the applicability and functionality of the velocity feedback vibration control system are discussed.

Integrated piezoelectric-based ultrasonic transducers (UTs) have been developed for potential structural health monitoring. Fabrication techniques and performance evaluation of these transducers at selected monitoring sites are presented. Our novel transducer fabrication approach focuses on the use of handheld and readily accessible equipment to perform sol–gel spray coating, including the use of a heat gun or a torch, to carry out drying and firing, poling and electrode fabrication. The application of these integrated UTs for thickness measurement of graphite/epoxy composites, thickness monitoring of ice build up on aluminum plates at low temperatures, viscosity measurement of a cooling oil flow at temperatures up to 160 °C and monitoring metal debris in cooling oil engines is demonstrated.

Reduced-order modal models of linear piezoelectric structures are useful in vibration control and health monitoring. We study experimental identification of the fundamental parameters of these modal models. We propose two identification techniques for estimating piezoelectric modal couplings and piezoelectric modal capacitances. Both methods are easily implementable and rely on elementary vibration tests. We show the application of these methods to a sample structure hosting multiple transducers.

Surface-modified titanium oxide nano-particles with sodium dodecyl sulfate (SDS) were prepared by means of hydrolyzation. The size distribution shows that the average size of the modified particles is about 120 nm. The energy dispersive spectrometry and spectrometry photo-electron spectra indicate that the SDS does exist on the surface of particles. It is demonstrated that the slope of the wettability curve of modified particles of about 120 nm in size is almost five times larger than that of unmodified particles. Rheological measurement shows that the yield stress of the electrorheological (ER) fluid with the modified particles can reach about 130 kPa under 4 kV mm⁻¹ DC electric field when the volume fraction is 56 vol%; this is greatly enhanced in comparison with that of an unmodified TiO₂ ER fluid. It is further considered that the enhancements in wettability, proper dielectric constant and dielectric loss due to the SDS modification make an important contribution to the strong ER effect. Furthermore, this modified TiO₂ ER fluid also shows excellent suspended stability compared with the unmodified TiO₂ ER fluid.

An inflatable boom is a fundamental structural part of inflatable space structures maintaining the expected configuration of the whole system, supporting external loads and guaranteeing the efficiency of the membrane surface. The inflatable structure is a thin film structure compactly packaged and expanded to the desired configuration by the internal gas pressure. But the structures can be easily distorted and even collapsed by wrinkling. In this study, the behavior of an inflatable boom structure is investigated numerically and experimentally. To achieve a better bending strength, the methodology to control the wrinkling growth and the deformed configuration of the inflatable boom structure with a shape memory alloy (SMA) wire actuator is developed. To understand the nonlinear behavior of an inflatable boom due to wrinkling, the structure is numerically modeled using the ABAQUS finite element program with a wrinkling algorithm developed based on the Miller–Hedgepeth membrane theory. To verify the present analysis method, the inflatable boom made of Kapton film is examined by the bending tests with various internal pressures. To delay the growth of wrinkling that rapidly deteriorates the bending strength of the inflatable boom, a SMA wire actuator is applied. SMA wires are attached on the edge of the inflatable boom and generate a recovery force to remove wrinkling and restore the deformation of the boom.

The knowledge of nano-material properties not only helps us to understand the extreme behaviour of small-scale materials better (expected to be different from what we observe from their bulk value) but also helps us to analyse and design new advanced functionalized materials through different nano technologies. Among these fundamental properties, the cohesion (binding) energy mainly describes most behaviours of materials in different environments. In this work, we discuss this fundamental property through a nano-thermodynamical approach using two algorithms, where in the first approach the size dependence of the inner (bulk) cohesion energy is studied, and in the second approach the surface cohesion energy is considered too. The results, which are presented through a computational demonstration (for four different metals: Al, Ga, W and Ag), can be compared with some experimental values for W metallic nano-particles.

Signal processing algorithms for guided wave pulse echo-based structural health monitoring (SHM) must be capable of isolating individual reflections from defects in the structure, if any, which could be overlapping and multimodal. In addition, they should be able to estimate the time–frequency centers, the modes and individual energies of the reflections, which would be used to locate and characterize defects. Finally, they should be computationally efficient and amenable to automated processing. This work addresses these issues with a new algorithm employing chirplet matching pursuits followed by a mode correlation check for single point sensors. Its theoretical advantages over conventional time–frequency representations for SHM are elaborated. Results from numerical simulations and experiments in isotropic plate structures are presented, which show the capability of the proposed algorithm. Finally, the issue of in-plane triangulation is discussed and experimental work done to explore this issue is presented.

In this paper we show increased interfacial bonding of a photoresist (SU-8) deposited onto highly polished poly(methyl methacrylate) (PMMA) substrates containing a UV absorber. We also demonstrate the facile sealing/covalent bonding of 100 µm × 20 µm PDMS replica microchannels, made from these PMMA/SU-8 moldings, onto thermally polymerized styrene. Sealing was achieved through radio-frequency plasma discharge (RFPD) oxygen plasma treatment.

A structure using the two-way shape memory effect (TWSME) returns to its initial shape by increasing or decreasing the temperature under initial residual stress. Through the thermo-mechanical constitutive equation of the shape memory alloy (SMA) proposed by Lagoudas et al (1996 Mech. Compos. Mater. Struct. 3 153–79), we simulate the behavior of a double SMA wire actuator in which two SMA wires are attached to the tip of a bar under the initially given residual stress. Through the numerical results conducted in the present study, the behavior and characteristics of an SMA actuator with two SMA wires are shown to be quite different from those of a single wire actuator, and the proposed actuator device is suitable for repeated actuation. A thermal cycle needs to be applied to the double SMA wire actuator for it to return to the original position. The proper thermal cycle for repeated actuation is proposed in the present study. The simulation algorithm proposed in the present study can be applied extensively to the analysis of the assembled system of SMA actuator and host structure in practical applications.

A novel optical fibre sensing system has been developed using fibre Bragg gratings embedded in a SmartRod structure based on pultruded composite rods. A thorough investigation of the mechanical reliability of the fibres, gratings and whole SmartRod structure was made. Techniques used included tensile testing, static fatigue in bend and dynamic fatigue in bend, in a variety of environments. The strength and interface properties of the whole structure were also tested. The mechanical reliability of the system was found to be very adequate for the proposed tunnel applications.

It is well known that cyclic fatigue induces hysteretic heating and temperature increase in polymer composite materials. Optical sensing technology is well developed to perform efficient in-field monitoring of the thermo-mechanical behaviour of engineering composite structures in sectors ranging from automotive to aerospace, where the implications of thermal fatigue are important. In this paper an experimental method and its results for temperature measurements in a glass/polypropylene composite beam subjected to cyclic bending at 6 Hz are reported. Since the sensors are sensitive to both temperature and strain, they are placed on the surface and in the centre of the specimen during processing, thus minimizing the effects of the mechanical strain during loading.

Temperature increases of 9 °C both inside and on the specimen surface are recorded with fibre Bragg grating (FBG) sensors and verified by full-field temperature analysis using infrared thermography on the surface and thermocouples on both the surface and through the thickness of the composite. Discrimination between relatively large dynamic strain (responsible for ∼280 pm Bragg wavelength shift oscillations), birefringence (responsible for ∼70 pm), and temperature variations (9 °C leads to a Bragg wavelength shift of ∼240 pm) is achieved by suitable integration of embedded FBGs and optical data processing. The achieved temperature resolution is 1 °C. The method outlined in this paper can be applied in various experimental configurations for temperature measurements in polymeric materials.

Lamb waves have great potential for structural damage detection in many engineering areas. However, the method requires some experience when complex structures are monitored. Deciding the optimal positions of transducers is one of the most important problems. Sensor location studies can be investigated using a number of signal processing techniques. This paper applies wave propagation modelling for the analysis of sensor positions in Lamb wave based damage detection. The problem is investigated using the local interaction simulation approach for Lamb wave propagation modelling in an aluminium plate with a rectangular damage slot and a fatigue crack. The study demonstrates that sensor location is important for clarity and physical understanding of propagating wave packages, good signal-to-noise ratio and reliable damage detection. All these elements can be investigated using numerical simulations.

This paper describes the design and performance testing of a micropositioning, vibration isolation and suppression system, which can be used to position a piece of equipment with sub-micrometre accuracy and stabilize it against various types of external disturbance. The presented demonstrator was designed as part of a novel extremely open pre-polarization magnetic resonance imaging (MRI) scanner. The active control system utilizes six piezoelectric actuators, wide-bandwidth optical fibre displacement sensors and a very fast digital field programmable gate array (FPGA) controller. A PID feedback control algorithm with emphasis on a very high level of integral gain is employed. Due to the high external forces expected, the whole structure is designed to be as stiff as possible, including a novel hard mount approach with parallel passive damping for the suspension of the payload. The performance of the system is studied theoretically and experimentally. The sensitive equipment can be positioned in six degrees of freedom with an accuracy of ± 0.2 µm. External disturbances acting on the support structure or the equipment itself are attenuated in three degrees of freedom by more than −20 dB within a bandwidth of 0–200 Hz. Excellent impulse rejection and input tracking are demonstrated as well.

In this paper we present control algorithms for novel electro-rheological fluid based resistive torque generation elements that will be used to drive the joint of a new type of portable and controllable active knee rehabilitation orthotic device (AKROD) for iso-inertial, isokinetic, and isometric exercising as well as gait retraining. The AKROD is composed of straps and rigid components for attachment to the leg, with a central hinge mechanism where a gear system is connected. The key features of AKROD include: a compact, lightweight design with highly tunable torque capabilities through a variable damper component, full portability with on-board power, control circuitry, and sensors (encoder and torque), and real-time capabilities for closed loop computer control for optimizing gait retraining. The variable damper component is achieved through an electro-rheological fluid (ERF) element that connects to the output of the gear system. Using the electrically controlled rheological properties of ERFs, compact brakes capable of supplying high resistive and controllable torques are developed. In this project, a prototype for the AKROD has been developed and tested. The AKROD's ERF resistive actuator was tested in laboratory experiments using a custom-made ERF testing apparatus (ETA). ETA provides a computer-controlled environment to test ERF brakes and actuators in various conditions and scenarios including emulating the interaction between human muscles involved with the knee and the AKROD's ERF actuators/brakes. The AKROD's ERF resistive actuator was tested in closed loop torque control experiments. A hybrid (non-linear, adaptive) proportional-integral (PI) torque controller was implemented to achieve this goal.

Since the discovery of carbon nanotubes, researchers have been fascinated by their mechanical and electrical properties, as well as their versatility for a wide array of applications. In this study, a carbon nanotube–polyelectrolyte composite multilayer thin film fabricated by a layer-by-layer (LbL) method is proposed to develop a multifunctional material for measuring strain and corrosion processes. LbL fabrication of carbon nanotube composites yields mechanically strong thin films in which multiple sensing transduction mechanisms can be encoded. For example, judicious selection of carbon nanotube concentrations and polyelectrolyte matrices can yield thin films that exhibit changes in their electrical properties to strain and pH. In this study, experimental results suggest a consistent trend between carbon nanotube concentrations and strain sensor sensitivity. Furthermore, by simply altering the type of polyelectrolyte used, pH sensors of high sensitivity can be developed to potentially monitor environmental factors suggesting corrosion of metallic structural materials (e.g. steel, aluminum).

This paper introduces integral resonant control, IRC, a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. By adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. It is shown that this modification permits the direct application of integral feedback and results in good performance and stability margins. By slightly increasing the controller complexity from first to second order, low-frequency gain can be curtailed, alleviating problems due to unnecessarily high controller gain below the first mode. Experimental application to a piezoelectric laminate cantilever beam demonstrates up to 24 dB modal amplitude reduction over the first eight modes.

Piezoelectric materials (PZT) have shown the ability to convert mechanical forces into an electric field in response to the application of mechanical stresses or vice versa. This property of the materials has found extensive applications in a vast array of areas including sensors and actuators. The study presented in this paper targets the modeling of a PZT bender for voltage and power generation by transforming ambient vibrations into electrical energy. This device can potentially replace the battery that supplies the power in a microwatt range necessary for operating sensors and data transmission. One of the advantages is that it is maintenance-free over a long time span.

The feasibility of this application has been repeatedly demonstrated in the literature, but a real demonstration of a working device is partially successful because of the various design parameters necessary for a construction of the PZT bender. According to a literature survey, the device can be modeled using various approaches. This paper focuses on the analytical approach based on Euler–Bernoulli beam theory and Timoshenko beam equations for the voltage and power generation, which is then compared with two previously described models in the literature: the electrical equivalent circuit and energy method. The three models are then implemented in a Matlab/Simulink/Simpower environment and simulated with an AC/DC power conversion circuit. The results of the simulation and the experiment have been compared and discussed.

This paper discusses a self-sensing vibration suppression method that measures only the value of the piezoelectric voltage. The method separates the electrical status into two cases concerning electrical current and characterizes each of these to establish a self-sensing system using extended system equations and a Kalman filter. Our self-sensing system can avoid estimation blackout during closed-circuit status and lessen harmful influences from residual modes. Experiments revealed that the self-sensing system suppressed vibrations in cooperation with state-switching and synchronized-switching controls. We confirmed that the self-sensing method is robust against model errors in a vibration suppression experiment in which there are model errors caused by an intentional frequency shift.

With increasing traffic volume follows an increase in the number of overheight truck collisions with highway bridges. The detection of collision impact and evaluation of the impact level is a critical issue in the maintenance of a concrete bridge. In this paper, an overheight collision detection and evaluation system is developed for concrete bridge girders using piezoelectric transducers. An electric circuit is designed to detect the impact and to activate a digital camera to take photos of the offending truck. Impact tests and a health monitoring test were conducted on a model concrete bridge girder by using three piezoelectric transducers embedded before casting. From the experimental data of the impact test, it can be seen that there is a linear relation between the output of sensor energy and the impact energy. The health monitoring results show that the proposed damage index indicates the level of damage inside the model concrete bridge girder. The proposed overheight truck–bridge collision detection and evaluation system has the potential to be applied to the safety monitoring of highway bridges.

The radial vibration of the combination of a thin piezoelectric ceramic disk and a thin circular metal ring that are clamped together in the radial direction is analyzed. This type of combination of a piezoelectric ceramic disk and a circular metal ring can be used as the active elements in moonie and cymbal transducers and actuators. In this paper, the radial vibrations of a thin piezoelectric ceramic disk and a thin circular metal ring are analyzed, and their radial electro-mechanical equivalent circuits are obtained, respectively. Based on electro-mechanical equivalent circuits and using the radial boundary conditions, the electro-mechanical equivalent circuit of the combination of a piezoelectric ceramic disk and a circular metal ring is given and its radial frequency equation is obtained. The relationships between the resonance frequency, the anti-resonance frequency, and the effective electro-mechanical coupling coefficient and the geometrical dimensions are analyzed. The radial vibrational velocity ratio or the radial vibrational velocity magnification is studied. It is illustrated that the theoretical radial resonance and anti-resonance frequencies from the frequency equation are in good agreement with the measured results.

The electromechanical performance of planar dielectric elastomer (DE) actuators is predicted by applying a novel model for the mechanical behavior of visco-hyperelastic films such as VHB 4910 (manufactured by 3M). The electrostatic pressure was introduced in the film thickness direction to adapt the film model to DE actuators. Moreover, the actuator was embedded in an appropriate electrical supply circuit to account for the electrodynamic effects.

The simulation of the active expansion of a biaxially prestrained, planar DE actuator configuration showed unstable deformation behavior under long-term activation. For activation voltages exceeding a critical level, the active expansion thus became uncontrolled after some time.

The model was also applied to a DE strip actuator configuration under sinusoidal electromechanical excitation. The influence of selected parameters on the overall actuator performance was thereby investigated. While the specific energy density increases with increasing amplitudes of the activation voltage and the stretch ratio, the optimum efficiency is predicted to lie at moderate electromechanical excitations.

A new experimental method for determining the x-ray elastic constants (S₁ and (1/2)S₂) of thin films is proposed. The curvatures of the single-crystal substrates before and after depositing thin films are first measured using a high-resolution x-ray rocking curve technique with high-quality monochromatic and high-intensity synchrotron radiation. The residual stresses in the films are then calculated from the change in substrate curvature based on the well-known modified Stoney's equation. The formulae for calculation of S₁ and (1/2)S₂ are deduced based on measured residual stress and the lattice spacing d_ψ versus sin²ψ curves before and after a mechanical loading, while the magnitude of the external loading does not need to be known. Values of (1/2)S₂ of films can even be obtained without loading. Pb(Zr_0.52Ti_0.48) and LaNiO₃ films grown on a single-crystal silicon substrate using pulsed laser deposition are employed to demonstrate the measurement method.

Magnetoelectric composites with ferrite–ferroelectric composition (x)Ni_0.8Zn_0.2Fe₂O₄+(1−x) PZT (lead zirconate titanate (PbZr_0.52Ti_0.48O₃) used as a ferroelectric phase) in which x varies as 0, 0.15, 0.30, 0.45 and 1 mol% were prepared by using a conventional ceramic double-sintering method. Phase analysis was carried out using the x-ray diffraction technique, which confirms a cubic spinel structure for the ferrite and tetragonal perovskite structure for the ferroelectric phase. The variation of the dielectric constant (ε') and loss tangent (tanδ) in the frequency range 20 Hz–1 MHz were studied. The conduction phenomenon is explained on the basis of a small polaron hopping model. The confirmation of this phenomenon was made with the help of ac conductivity measurements. The dc resistivity was measured as a function of temperature in the range from room temperature to 800 °C. Hysteresis measurements were performed to determine the saturation magnetization (M_s) and magnetic moment (ηB). The static magnetoelectric conversion factor (dE/dH)_H was measured as a function of the magnetic field. All composites show a linear decrease of magnetoelectric conversion in the presence of a static magnetic field.

Using piezoelectric elements to harvest energy from ambient vibrations has been of great interest over the past few years. Due to the relatively low power output of piezoelectric materials, energy storage devices are used to accumulate harvested energy for intermittent use. Piezoelectric energy harvesting circuits have two schemes: one-stage and two-stage energy harvesting. A one-stage energy harvesting scheme includes a conventional diode bridge rectifier and an energy storage device. In recent years, two-stage energy harvesting circuits have been explored. While the results shown in previous research and development are promising, there are still some issues that need to be studied. Energy storage devices such as rechargeable batteries and supercapacitors have different cell voltages. Moreover, the storage cells can be connected in series to increase the voltage range. The storage device voltage is an important factor that influences the energy harvesting efficiency. This paper will study the efficiencies of the energy harvesting circuits considering the storage device voltages. For one-stage energy harvesting, expressions are derived to calculate the efficiencies towards different storage device voltages and verified by experiments. For two-stage energy harvesting circuits, theoretical efficiency expressions are derived and verified by PSPICE simulations. These two energy harvesting schemes are also compared. The results show that a one-stage energy harvesting scheme can achieve higher efficiency than the two-stage scheme towards a range of energy storage voltages.

Magnetorheological elastomers (MRE) are interesting candidates for active vibration control of structural systems. In this study, spring elements consisting of magnetorheological elastomer were prepared and tested in dynamic compression to study the changes in their stiffness and vibration damping characteristics under the influence of a magnetic field. Aligned and isotropic magnetorheological elastomer composites were prepared using room temperature vulcanizing silicone elastomer as the matrix material and carbonyl iron as the magnetizable filler. Aligned MREs were prepared by curing the material under an external magnetic field. Aligned MREs were tested and the results were compared with isotropic composites with no preferred orientation.

The mechanical properties of the MREs were tested in cyclic compression passively and with increasing magnetic flux density. The influence of the testing frequency and strain amplitude on the dynamic stiffness and damping properties was studied. It was noted that when measured in a magnetic field both the dynamic spring constants and the loss factor values of aligned MREs were increased compared to the zero-field values. The dynamic stiffness of aligned MREs increased with increasing testing frequency and it was tunable with magnetic flux density in the studied frequency range. The loss factor of aligned MREs was also tunable with the magnetic flux density but the absolute values also depend on the testing frequency. The dynamic stiffness of the aligned MREs measured in compression decreased with increasing strain amplitude, but the damping properties were not affected similarly. On the basis of these results, MREs are applicable as tunable spring elements for active vibration control.

Impact-induced damage in fiber-reinforced laminated composite plates is characterized. An instrumented impact tower was used to carry out low-velocity impacts on thirteen clamped glass/epoxy composite plates. A range of impact energies was experimentally investigated by progressively varying impactor masses (holding the impact height constant) and varying impact heights (holding the impactor mass constant). The in-plane strain profiles as measured by polyvinylidene fluoride (PVDF) piezoelectric sensors are shown to indicate damage initiation and to correlate to impact energy. Plate damage included matrix cracking, fiber breakage, and delamination. Electronic shearography validated the existence of the impact damage and demonstrated an actual damage area larger than visible indications. The strain profiles that are associated with damage were replicated using an in-house finite element code. Using these simulated strain signatures and the shearography results, a backpropagation artificial neural network (ANN) is shown to detect and classify the type and severity of damage.

A low power sensor read-out circuit has been implemented in 0.35 µm CMOS technology that consumes only 400 µW of power and occupies an area of 0.66 mm². The circuit is capable of converting the current signal from any generic biosensor into an amplitude shift keying (ASK) signal. The on-chip potentiostat biases the chemical sensor electrodes to create the sensor current which is then integrated and buffered to generate a square wave with a frequency proportional to the sensor current level. A programmable frequency divider is incorporated to fix the ASK envelope frequency to be inbetween 20 Hz and 20 kHz, which is within the audible range of human hearing. The entire transmitter block operates with a supply voltage as low as 1.5 V, and it can be easily powered up by an external RF source. Test results emulate the simulation results with good agreement and corroborate the efficacy of the designed system.

Cantilever beams, made of shape memory alloy (SMA), undergo much larger deflection in comparison to those made of other materials. Again, cantilever beams with reducing cross section along the span show much larger deflections compared to those of constant cross section beams. Analysis was conducted for such a cantilever beam with reducing cross-sectional area made of SMA, taking into account its highly nonlinear stress–strain curves. A computer code in C has been developed using the Runge–Kutta technique for the purpose of simulation. For rigorous analysis, the true stress–strain curves in tension as well as in compression have been used for the study. Moment–curvature and reduced modulus–curvature relations are obtained from the nonlinear stress–strain relations for different sections of the beam and used in the simulation. It is seen that load–deflection curves are initially linear but nonlinear and convex upward at a high load. Furthermore, the compressive stress in the beam is significantly higher than the tensile stress because of asymmetry. Interestingly, for the different cases considered, it is found that part of the SMA beam material may remain in the parent austenite phase, mixed phase or in the stress-induced martensitic phase. Importantly, it is found that more material can be removed from an SMA beam of uniform strength, originally designed without considering geometric nonlinearity and the effect of end-shortening. Comparison of the numerical results with the available theory shows very good agreement, verifying the soundness of the entire numerical simulation scheme.

Mechanical components of sandwiched piezoelectric transducers are modeled using one-dimensional wave transmission and piezoelectric equations. Using the impedance method, resonance frequencies, stress and displacement distributions along the multilayered piezoelectric transducers of different dimensions and materials are obtained. The calculated resonance frequencies and the impedances are experimentally verified. For ultrasonic welding of plastics, the effect of the parts to be welded on the resonance frequency of the whole system is investigated regarding both material damping and piezoelectric losses. Using the methods developed, several piezoelectric transducers are analysed for different designs. The obtained results can be used to better understand the qualitative relations between the design variables of ultrasonic piezoelectric transducers.