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To explore the subacromial motion metrics in patients with and without subacromial impingement syndrome (SIS) and to investigate whether the abnormality was associated with rotator cuff pathologies.This cross-sectional observational study used dynamic quantitative ultrasonography imaging for shoulder joint assessment.Outpatient rehabilitation clinic.Individuals with SIS on at least 1 shoulder (n=32) and asymptomatic controls (n=32) (N=64).Not applicable.Frame-by-frame, the humeral greater tuberosity against the lateral edge of the acromion was traced to obtain the minimal vertical acromiohumeral distance (AHD). The rotation angle and radius of the humerus were computed using the least-squares curve fitting method.Approximately two-thirds of the shoulders with SIS did not have any sonographically identifiable rotator cuff pathologies. There was a consistent trend of nonsignificantly increased humeral rotation angles in painful shoulders. The generalized estimating equation demonstrated that the decreased minimal vertical AHD was associated with painful subacromial impingement (β coefficient: -0.123cm, 95% confidence interval [CI], -0.199 to -0.047). The area under the curve for the minimal vertical AHD to discriminate painful or impinged shoulders ranged from 0.624-0.676. The increased rotation angle (β coefficient: 10.516°; 95% CI, 3.103-17.929) and decreased rotation radius (β coefficient: -2.903cm; 95% CI, -5.693 to -0.111) were shown to be significantly related to the presence of supraspinatus tendinopathy.Shoulders with SIS were characterized by a decreased minimal vertical AHD during dynamic examination. Abnormal subacromial metrics can develop in patients with mild (or no) rotator cuff pathologies. More prospective cohort studies are warranted to investigate the changes in subacromial motion metrics in populations at risk for painful or impinged shoulders.

A cantilever beam-based vibration energy harvester is generally preferred due to its simplicity and effectiveness as compared to a spring mass system. This paper analyses the use of a spring to amplify the performance of a conventional single degree of freedom (SDOF) cantilever beam-based vibration energy harvester. A spring was introduced to modify the conventional SDOF design into a two single degree of freedom (2SDOF) system and a two degree of freedom (2DOF) system. The motion of the spring was restricted in the vertical motion using a slider and a linear guide rail fixed to the vibrating base, hence introducing a dynamic friction into the system. Both designs were analysed under three different cases to observe the effect of natural frequency reduction on the frequency bandwidth and power harvested by each design. The vibration-friction interaction in the designs was modelled based on the concept of relative motion. Two different friction theories were applied and verified with simulation and experiment. It was shown that the stick condition would not occur in a SDOF system with a dynamic friction interaction. It was also found that it is possible to tune the friction force of a dynamic friction surface to induce a favourable output at the isolation frequencies of a 2DOF system. Analysis shows that the 2DOF design displayed a larger power density than the conventional SDOF design below a certain natural frequency value, being 78.1% higher at 9.5 Hz. The power densities of the 2SDOF design were almost similar to the SDOF design. However, the 2SDOF design displayed a significant drop in power when under the condition of matched natural frequencies. Nevertheless, the frequency bandwidth of the 2SDOF design can be improved by tuning its two resonant peaks closer to each other.

This paper presents a novel and simplified method to predict the damping ratio and power output of a cantilever-based electromagnetic vibration energy harvester through finite element analysis. A strong relationship was determined between the mechanical damping of a structure and the resonant stress at the clamped end of the structure under critically damped condition, otherwise described as the critically damped stress. This relation was used as a basis to develop a material-specific damping stress equation. The equation was then integrated into FEA to analyse a certain electromagnetic vibration energy harvester design by considering the variation in damping and power output for every structural change. The effect of the phase difference on the power output of the electromagnetic harvester was also considered. The FEA design that recorded the highest power output prediction (11.1% higher than the initial structure) was then verified experimentally, displaying a good agreement with experimental results, recording an error of less than 5.0% for the amplitude and voltage evaluation and 8.0% for the power output assessment. Hence, this validates the accuracy of the proposed method in predicting not only the mechanical damping of regular cantilever beams, but also other cantilever beam-based structures.

The article presents the development of a self-powered rectified electromagnetic energy harvester (EMEH) under low frequency excitations. To overcome the drawback of low output voltage across the small optimal load, it is proposed to use the transistor-based rectifier biased by the self-powered SECE-based piezoelectric energy harvester (PEH). In addition, the buck-boost converter controlled by the self-powered SSHI-based PEH is im- plemented for the maximum power point tracking. A semi-analytic model is developed for predicting the peak power and the optimal load used for designing the buck-boost converter. The prediction is then validated by experiment showing 1.5 mW optimal output power. Further, it is found that the 0.22 low rectified voltage is increased up to 2.5 V by the proposed SSHI-based voltage boosting technique. It offers advantages of zero quiescent power dissipation and the ease of tuning the input impedance of the buck-boost converter by varying the SSHI load impedance.

Many biological materials such as bone, teeth and nacre exhibit superior mechanical strength and toughness. These materials share similar hierarchical arrangement that stiff blocks are embedded in a soft matrix. For example, the sophisticated brick-and-mortar design in nacres can effectively increase the fracture toughness by a factor of 3,000 compared to its major component – mineral. Although extensive studies have been done attempting to understand the toughening of the nacre-like materials, the underlying mechanisms associated with crack behaviors are not fully clear yet. This study applies the phase-field method for crack behaviors in both layered structure and nacre-like materials to distinguish the importance of the commonly observed toughening mechanisms. First, we investigate the toughening of a simple layered structure, where the surfing boundary condition is imposed to suppress the crack deflection. We compute the maximum energy release rate using the J-integral technique to find out that the effective fracture toughness is much less than the experimentally measured fracture toughness of these bio- composite materials. Then we investigate the crack growth in a nacre-like material to obtain a phase diagram summarizing four different modes of crack growth: straight crack, interface crack, branching, and crack arrest for a range of structural parameters relevant to nacres, including the aspect ratio, volume fraction of mineral, elastic modulus mismatch and fracture resistance mismatch. Our results clarify the relation between the complex hierarchical microstructure and the toughening mechanisms, such as crack bridging, microcracking and tablet sliding.

The article presents the study of a novel self-powered SECE (synchronized electric charge extraction) circuit for scavenging piezoelectric energy under low-frequency shock excitation. Specifically, the device consists of a piezoelectric cantilever beam whose tip magnet is impulsively excited by a rotating magnet. It is attached to a load-independent SECE circuit with the advantage of power enhancement at low-level output voltage. The proposed circuit includes an envelope detector for voltage detection, a voltage divider for minimizing the switching delay and a diode for recovering the charge on the detection capacitance. The result shows that the predicted harvested power agrees well with the experimental observations. In addition, the power ripples are significantly reduced due to the larger electric-induced damping drawn from the SECE technique. Finally, the load-independent property makes the observed SECE power remain constant within the output voltage operated at around 2-5 volt, and therefore outperforms the standard DC power.

This paper presents the techniques for formulating the multiple segmented smart plate structures with different circuit connection patterns using the electromechanical finite element dynamic analysis. There are three major contributions in the proposed numerical studies. First, the electromechanical discretization has been developed for generalizing the coupled system of Kirchhoff’s smart plate structures with circuit connection patterns. Such constitutive numerical models reduced from the extended Lagrange equations can be used for the physical systems including, but not restricted to, the multiple piezoelectric and electrode segments. Second, the multiple piezoelectric or electrode segments can be arranged electrically in parallel, series, and mixed series–parallel connections with the on–off switching techniques where the electrical outputs of each connection are further connected with the standard AC–DC circuit interfaces. Third, the coupling transformation technique (CTT) has been introduced by modifying the orthonormalized global element matrices into the scalar form equations. As a result, the multimode frequency response function and time-waveform signal response equations are distinctly formulated for each circuit connection. Further parametric numerical case studies are also discussed in this paper. The benefit of using the circuit connection patterns with the on–off switching techniques is that the studies can be used for an adaptive vibration power harvester.

The article investigates various cantilever configurations for energy harvesting from rotational motion. A piezoelectric cantilever beam is mounted radially on a rotating body with different configurations. A harvester of type A (type B) refers to an outward (inward) configuration of beam with the direction of the transverse vibration perpendicular to the rotational axis. On the other hand, a rotary harvester of the type C is an outward beam with the transverse vibration in parallel to the rotational axis. A unified approach based on the Hamiltonian principle is employed and the methodology for deriving the formulations is based on the distributed parameter method. The result shows that both the type A and type C enjoy the feature of passive self-tuning of resonance. But the type C exhibits better ability in tuning than the type A. In addition, the type B shows significant harvested power at the cost of loss of tuning ability

The paper studies the electrical response of an array of piezoelectric oscillators attached to the synchronized electric charge extraction (SECE) interface circuit. The analytic estimate of output power is derived and presented through the matrix formulation of generalized Ohm’s law (charging on capacitance) for the case of parallel (series) connection of energy harvesters. These formulations mainly depend on the proposed equivalent load impedances which are independent of external resistive loads. It therefore offers an advantage of enabling harvested power independent of DC output voltage and making the harvester array desirable for broadband energy scavenging. The proposed framework is subsequently validated both numerically and experimentally. The results show that the power output and bandwidth of an SECE-based array are superior to that based on the standard energy harvesting circuit. Further, it is found that the behavior of an SECE array electrically arranged in parallel connection is different from that connected in series. The former demonstrates the output power higher than the latter, while the latter exhibits roughly uniform peak power in frequency response. However, the experiment indicates the unexpected power drop deviated significantly from the prediction in the array of harvesters connected in series. Such a discrepancy is explained as a result of comparatively serious leakage current in the reverse-biased diodes.

This paper focuses on the primary development of novel analytical and numerical studies for the smart plate structure due to the effects of point mass locations, dynamic motions, and network segmentations. Instead of the alternative capabilities in active and passive control systems, the technical application of the present work can also be found in the energy harvesting system. The simplified theoretical studies have shown the simultaneous derivations with full variational parameters. In particular, these parameters consist of the mechanical and electromechanical systems, the mixed series–parallel electrode segment connection, and the harvesting circuit. The mechanical system parameters include elasticity with stress-strain relation, internal damping stress, air damping, and dynamics of the integrated physical system. The electromechanical system parameters include electrical displacement, electrical stress and electric-polarity field of the piezoelectricity. For the analytical approach, the governing equations of motion based on the Gram-Schmidt iterative process have been derived using the extended Hamiltonian principle and Ritz method-based weak form system. For validation, the electromechanical finite element equations reduced from the extended Lagrange’s equations have been developed using electromechanical discretisation and coupling transformation techniques. As a result, the two theoretical models have shown distinct frequency response equations for the dynamic solutions of the integrated physical system. In parametric studies, the two theoretical models of the smart plates with variable geometrical aspect ratio and different locations of point mass are discussed, giving good agreement. The strain mode analysis is utilised to identify the shape patterns at the region of the smart plate due to the change of strains. As a result, it can affect the electric power productions at the frequency domain. At certain cases, the appearance of asymmetric strain mode shapes may occur, resulting in the electric power reductions. To alleviate such condition, the activation of arbitrary electrode segments using the network connection can be implemented. Moreover, the smart structural model with different point mass locations is also subjected to the base excitation and the dynamic force. The proposed technique can adaptively and accumulatively generate the optimal power outputs and shift the resonance frequencies. All results of the parametric studies quantitatively show the dynamic system behaviours.

This paper presents an adaptive dynamic analysis of discontinuous smart beam energy harvester systems using a shunt vibration control. The smart structural systems, connected with the shunt and harvesting circuit interfaces, consist of the three types of non-homogeneous structural combinations with different piezoelectric materials. The constitutive coupled dynamic equations with full variational parameters are reduced using the charge type-based Hamiltonian mechanics and the Ritz method-based weak-form analytical approach. Unlike the conventional techniques, this study elaborates the appearance of the two resonances with a wider shift on a specific range of the optimal power output frequencies, using only the first mode of the smart structural systems. Moreover, the two-equal peak of the optimal response may potentially occur to appear not only at the first resonance, but also at the second resonance. This intrinsically represents strong electromechanical effect, depending on the properties and thicknesses of piezoelectric materials and the circuit parameters. The accuracy of the theoretical method is tested using the iterative computational process of the optimal frequency response with full coupled electromechanical system parameters. Further details of the parametric studies are discussed to show the prediction of the energy harvesting with the ability of tuning an adaptive frequency response.

This paper proposes a broadband rotational energy harvesting setup by using micro piezoelectric energy harvester (PEH). When driven in different rotating speed, the PEH can output relatively high power which exhibits the phenomenon of frequency up-conversion transforming the low frequency of rotation into the high frequency of resonant vibration. It aims to power self-powered devices used in the applications, like smart tires, smart bearings, and health monitoring sensors on rotational machines. Through the excitation of the rotary magnetic repulsion, the cantilever beam presents periodically damped oscillation. Under the rotational excitation, the maximum output voltage and power of PEH with optimal impedance is 28.2 Vpp and 663 μW, respectively. The output performance of the same energy harvester driven in ordinary vibrational based excitation is compared with rotational oscillation under open circuit condition. The maximum output voltage under 2.5g acceleration level of vibration is 27.54 Vpp while the peak output voltage of 36.5 Vpp in rotational excitation (in 265 rpm).

The paper is focuses on the development of a theoretical framework together with an experimental validation to investigate rotational piezoelectric energy harvesting. The proposed device includes an electrically rectified piezoelectric bimorph mounted on a stationary base with a magnet attached to its free end. Energy is harvested by vibration of beam induced by non-contact rotary magnetic plucking. The DC power frequency response is predicted and found to be in good agreement with experiment. It shows that the harvested DC power is around 1 mW in average with the rotational frequency ranging from 5 Hz to 14 Hz. In addition, the parallel connection of two piezoelectric oscillators with respective electrical rectification is considered. It is observed that the power output of the array is the addition of the response from each individual piezoelectric oscillator.

This article proposes a framework for determining the types of nonlinearity observed in the frequency response of microscale energy harvesters made of a piezoelectric film deposited on a stainless-steel substrate. The model accounts for inertial, geometrical and material nonlinearities due to amplified excitation and induced hysteresis. The simulations based on the multiple scale analysis reveals the softening type of nonlinearity for the case of a 15 μm PZT thick film deposited on a 60 μm stainless-steel substrate. They agree quite well with the experimental observations. In addition, the further investigation shows the existence of the critical film thickness such that the hardening (softening) nonlinearity is observed if the film thickness is below (above) this critical value. It is also found that such a key parameter is mainly affected by the ratio of the bending stiffness due to material nonlinearity to that based on linear moduli. Finally, the hardening type of nonlinearity was also observed in different samples with very small film thickness, as predicted by the proposed framework.

In the conventional model of general vibration energy harvesters, the harvesting effect was regarded as only the electrically induced damping. Such intuition has overlooked the detailed dynamic contribution of practical power conditioning circuits. This paper presents an improved impedance model for the electromagnetic energy harvesting (EMEH) system considering the detailed dynamic components, which are introduced by the most extensively used full-wave bridge rectifier. The operation of the power electronics is studied under harmonic excitation. The waveforms, energy cycles, and impedance picture are illustrated for showing more information about the EMEH system. The theoretical prediction on harvesting power can properly describe the changing trend of the experimental result.

This paper presents the design and implementation of a series-SSHI-phi interface circuit for piezoelectric energy harvesting with improved operating frequency range. Adopting a nonlinear switching architecture, complex impedance matching can be achieved at off-resonance by introducing delay into switching timing. A buck-boost converter following the rectifier is used for resistive-load emulation and energy transfer. Implemented with a 0.25-μm CMOS HV process, experimental results with a commercially available piezoelectric device show a 56.1% improvement in 3-dB bandwidth compared to conventional series-SSHI interface. Furthermore, a 163% improvement in extracted power is demonstrated with −2% of frequency mismatch. When vibrating at resonant frequency of 126.7 Hz with 0.5 g acceleration and a 1.1-g tip mass, the harvester is able to extract 165 μW after considering the 12 μW of control power.

The article studies the behavior of a mixed parallel-series connection of piezoelectric oscillators attached to the standard interface for wideband energy harvesting. The estimate of power output is obtained analytically considering the formulations of balance of charge, energy and system dynamics. It can be presented based on the generalized matrix formulation of charging on capacitance in terms of equivalent load impedance. The proposed model is subsequently validated numerically through circuit simulations. Finally, a design with a careful choice of parallel-series mixed connection of oscillators is proposed for illustration. With a proper circuit layout triggering the switching of connection, the result shows that the peak power of each array configuration is roughly uniform within the frequency range of interest. Hence, the bandwidth is enlarged without the loss of peak power.Copyright © 2016 by ASME

This article presents the modeling of nonlinear response of micro piezoelectric energy harvesters under amplified base excitation. The micro transducer is a composite cantilever beam made of the PZT thick film deposited on the stainless-steel substrate. The model is developed based on the Euler-Bernoulli beam theory considering geometric and inertia nonlinearities, and the reduced formulation is derived based on the Hamiltonian variational principle. The harmonic balance method is used to simulate the nonlinear frequency response under various magnitudes of excitation and electric loads. The hardening type of nonlinearity is predicted and is found to be in good agreement with experiment. However, the softening response is also observed in different samples fabricated under different conditions. Such disagreement is under investigation.

Transforming materials with evolving microstructures is one of the most important classes of smart materials that have many potential technological applications, and an unconventional phase field approach based on the characteristic functions of transforming variants has been developed to simulate the formation and evolution of their microstructures. This approach is advantageous in its explicit material symmetry and energy well structure, minimal number of material coefficients, and easiness in coupling multiple physical processes and order parameters, and has been applied successfully to study the microstructures and macroscopic properties of shape memory alloys, ferroelectrics, ferromagnetic shape memory alloys, and multiferroic magnetoelectric crystals and films with increased complexity. In this topical review, the formulation of this unconventional phase field approach will be introduced in details, and its applications to various transforming materials will be discussed. Some examples of specific microstructures will also be presented.

Mixed phases of rhombohedral and tetragonal ferroelectric variants have been recently observed to coexist through epitaxial constraints in bismuth ferrite films. They form stripe-like domain patterns with orientations closely parallel to the substrate edges and exhibit unusually large piezoelectric response in the stripe areas. Here a model is developed for explaining the peculiar domain orientations as well as the enhancement of piezoelectricity in the mixed phase. The former is determined by the relative magnitudes of elastic and depolarization energy, whereas the latter is ascribed to the strain-driven softening in dielectric stiffness. The predictions show the similar trend as those observed in recent experiments.

Ferromagnetic shape memory alloys (FSMAs) possess coupled ferroelastic and ferromagnetic orderings simultaneously, making it possible to manipulate ferroelastic twins of FSMAs via a magnetic field or magnetic domains via mechanical loading. In this paper, we develop a phase-field model to simulate the formation and evolution of magnetoelastic domains in FSMAs under combined mechanical and magnetic loadings, taking into account both variant rearrangement and magnetization rotation. It is found that the large magnetic field induced strain in FSMAs results from a variant rearrangement process, yet such variant rearrangement can be blocked by a relatively large compressive stress, substantially reducing the magnetic field induced strain. Furthermore, either pseudoelastic or quasiplastic behavior is exhibited in FSMAs subjected to varying compressive stress, depending on the strength of the constant magnetic field applied. These results agree well with experiments, and can be used to guide the design and optimization of FSMAs.

Multiferroic materials possess electric and magnetic orderings simultaneously, making it possible to manipulate the electric state of a multiferroic by magnetic field, or vice versa. Among all single-phase multiferroics, BiFeO3 is particularly exciting, for its room temperature multiferroicity, excellent ferroelectric properties, and recently demonstrated electric control of antiferromagnetic domains, which opens door for its applications in spintronics. In this paper, we report a systematic theoretical and computational study on the structure and evolution of magnetoelectric domains in multiferroic BiFeO3. A continuum description is developed for antiferromagnetic ordering first, which is then incorporated into an unconventional phase field method that couples ferroelastic, ferroelectric, and antiferromagnetic orderings through the characteristic function of variants. The internal elastic, electric, and magnetic fields are carefully analyzed, taking into account both bulk and thin film geometries and boundary conditions. The theory is implemented into numerical simulations, where we not only observe the coupled ferroelectric and antiferromagnetic domains, and demonstrate the electric control of antiferromagnetic ordering, but also reveal the switching of antiferromagnetic domains by mechanical stress that is yet to be reported in experiment. Our study offers deep insight into the microstructural evolution and macroscopic properties of BiFeO3, and provides a powerful tool to study a wide range of multiferroic materials with magnetoelectric coupling.

Large strain actuation in barium titanate (BaTiO3) single crystals subjected to combined uniaxial stress and electric field is examined. A maximum strain of about 0.45% is measured under a combined loading of 2.7 MPa compressive stress and ±1.25 MV m −1 cyclic electric field. Above 2.7 MPa, the crystal does not cycle fully between the in-plane and out-of-plane polarized states due to large compressive stress, and consequently, a considerable reduction in actuation strain is apparent. The hysteresis evolution of the crystal under combined electromechanical loading reveals incomplete switching characteristics and a considerable disproportion of slope gradients at zero electric field for the measured polarization and strain hysteresis curves. A likely cause for the disproportion of slope gradients is the cooperative operation of multiple 90 ◦ switching systems by which “polarization-free” strain changes are induced. An in situ domain observation study reveals the formation of bubble-like micro-domains prior to the macroscopic 90◦ switching of the crystal bulk. The presence of these bubble-like “switching weak points” indicates that regions within the BaTiO3 single crystal do not necessarily switch 90

A novel multivariant model of martensite is developed through competing energetics to describe the coarsening, refinement and selection of the microstructure. In contrast with the conventional phase-field methods, a new set of field variables motivated by the hierarchical structure of multirank laminates is employed to represent each variant. As a result, the energy-well structure can be expressed explicitly in an elegant and unified fashion. The framework is applied to the investigation of pattern formation in martensitic thin films with trigonal symmetry. Various intriguing patterns are predicted and are found to be in good agreement with those observed in experiments. In addition, film orientations and patterns necessary to achieve large actuation strains are suggested for dome-shaped and tunnel-shaped microactuators. It is found that the resulting morphologies evolve with coherent interfaces under various loading conditions. This suggests that compatible walls provide a low-energy path during evolution, and the understanding of them leads to novel strategies of large strain actuation.

This article documents both modeling and experimental studies developed to investigate the switching behavior of ferroelectric single crystals. The theoretical model makes a priori ansatz that switching follows the evolution of a particular domain pattern. The choice of this configuration is dictated by the requirement that domains remain compatible during evolution, giving rise to a low-energy path for the overall switching. The construction of this pattern is achieved using multirank laminates. It offers an advantage of specifying different types of domain wall movements, leading to a distinction for the switching types. A loading experiment is performed on a barium titanate (BaTiO3) single crystal with a constant compressive stress and a cyclic electric field. Both 180 � and 90 � coercive fields are measured as input parameters required for the theoretical framework. The simulation results show good agreement with the observed strains measured by the present and other available experiments. It is found that depolarization has a non-trivial influence on attainable actuation strains. r 2008 Elsevier Ltd. All rights reserved.

This paper provides an analysis for the performance evaluation of a piezoelectric energy harvesting system using the synchronized switch harvesting on inductor (SSHI) electronic interface. In contrast with estimates based on a variety of approximations in the literature, an analytic expression of harvested power is derived explicitly and validated numerically for the SSHI system. It is shown that the electrical response using an ideal SSHI interface is similar to that using the standard interface in a strongly coupled electromechanical system operated at short circuit resonance. On the other hand, if the SSHI circuit is not ideal, the performance degradation is evaluated and classified according to the relative strength of coupling. It is found that the best use of the SSHI harvesting circuit is for systems in the mid-range of electromechanical coupling. The degradation in harvested power due to the non-perfect voltage inversion is not pronounced in this case, and a new finding shows that the reduction in power is much less sensitive to frequency deviations than that using the standard technique.

This paper presents the development of wideband energy harvesting by the parallel connection of multiple piezoelectric oscillators attached to a synchronized electric charge extraction (SECE) interface circuit. It is shown that the electric response is determined by the matrix formulation of generalized Ohm’s law. The impedance matrix is explicitly expressed in terms of the equivalent load impedance and system parameters. In addition, the load impedance is found to be independent of external load, so is harvested power. The framework is subsequently validated numerically by SPICE circuit simulations. Finally, the performance evaluation is carried out with comparisons to other interface circuits, including the standard and synchronized switch harvesting on inductor (SSHI) interfaces. The result demonstrates that the bandwidth of an SECE array system is improved and its harvested power is not less than that based on the use of other interface circuits.Copyright © 2015 by ASME

This paper studies the energy conversion efficiency for a rectified piezoelectric power harvester. An analytical model is proposed, and an expression of efficiency is derived under steady-state operation. In addition, the relationship among the conversion efficiency, electrically induced damping and ac–dc power output is established explicitly. It is shown that the optimization criteria are different depending on the relative strength of the coupling. For the weak electromechanical coupling system, the optimal power transfer is attained when the efficiency and induced damping achieve their maximum values. This result is consistent with that observed in the recent literature. However, a new finding shows that they are not simultaneously maximized in the strongly coupled electromechanical system.

Power harvesting refers to the practice of acquiring energy from the environment which would be otherwise wasted and converting it into usable electric energy. Much work has been done on studying the optimal AC power output, while little has considered the AC–DC output. This article investigates the optimal AC–DC power generation for a rectified piezoelectric device. In contrast with estimates based on various degrees of approximation in the recent literature, an analytic expression for the AC–DC power output is derived under steady-state operation. It shows that the harvested power depends on the input vibration characteristics (frequency and acceleration), the mass of the generator, the electrical load, the natural frequency, the mechanical damping ratio and the electromechanical coupling coefficient of the system. An effective power normalization scheme is provided to compare the relative performance and efficiency of devices. The theoretical predictions are validated and found to be in good agreement with both experimental observations and numerical simulations. Finally, several design guidelines are suggested for devices with large coupling coefficient and quality factor.

We have developed a framework based on micromagnetics to explore the effect of stress on the magnetostrictive behavior in ferromagnetics. Our approach is different from the conventional one which simply replaces the total strain by magnetostrain. Question arises for such an approach because of the loss of strain compatibility. Here, we have included the kinematic constraints in our micromagnetic model and developed a modified boundary integral formalism to calculate the intrinsic stress induced by incompatible magnetostrain. We have shown that for small magnetostriction of the order of 10 −5 , the results predicted by the present approach are slightly different from those predicted by the conventional method. But we have found that for large magnetostriction around 10 −3 order of magnitude, the conventional approach is insufficient to predict magnetic domain patterns and hysteresis precisely, and the effective magnetic field induced by intrinsic stress cannot be neglected.

Motivated by many experimental efforts to develop suitable shape-memory micropumps, we propose a multiscale framework to study the behavior of pressurized films. We use recoverable deflection as a measure to design large stroke micropumps and develop a model to estimate it. We show that the recoverable deflection of a polycrystalline shape-memory film depends on the transformation strain of the underlying martensitic transformation, the texture and especially on the size effects. We find that flat grains are preferable to long grains in columnar films concerning the purpose of large recoverable strain. We also show that common sputtering texture is not ideal for recoverable deflection in both Ti-Ni and Cu-based shape-memory films. It turns out that{100} Cu-based films may have better behavior than Ti-Ni films. We conclude with comparison with experiment. The interest in microelectromechanical system (MEMS) applications has recently motivated many experimental efforts to develop suitable microactuators and micropumps. These devices have a wide range of applications in fields such as drug delivery, inkjet printing and cooling systems of elec- tronic circuits. However, common MEMS-integrated actua- tion scheme has enjoyed limited success in delivering a rea- sonable work output from the extremely small size of devices, and therefore both high stroke and force are the key require- ment for selecting actuating materials. Shape-memory alloys show great promise in this aspect since their work density is significantly higher than that of other types of materials. 26) These alloys are able to recover large strain and are capable of high force, which in turn directly transmit large stoke and high pressure in micropumps. In addition, the disadvantage of low response rate caused by cooling and heating bulk shape- memory alloys can be greatly improved at small scales be- cause of the increase in the surface area to volume ratio. This makes these alloys in the form of thin films ideal for use in MEMS-integrated actuation scheme, and we seek to develop a micromechanical model to understand the behavior of film at an extremely small thickness. In this paper, we propose a framework to study the behavior of pressurized shape-memory thin films with intended appli- cation to large stoke micropumps. Our work was motivated by the recent experiment on the fabrication of SMA actuated micropumps. 16, 17, 26) They have reported that a Ti-Ni microp- ump exhibits the largest work out per cycle per unit volume amongst various common actuator systems. 26) However, the ratio of the deflection to the half-edge length of diaphragm has been observed around several values from 0.04 to 0.12 which only correspond to 0.2%-1.4% small strain. Our the- oretical prediction is around 0.15 which is larger than these experimental observations, and the discrepancy is not com- pletely understood here. We believe there should be a plenty of room to improve this critical ratio to design large stroke mi- cropumps. In particular, we show that {100} Cu-based shape

We study strain relief by surface roughness and composition variation in a stressed alloy film. Instead of using common perturbation techniques, we derive a rigorous relaxation formula based on the energy approach in the case of slightly undulating surface and fluctuating composition. We do not require any a priori assumption of elastic isotropy or identical material properties between film and substrate in deriving our result. We show that the change of elastic energy is negative, giving rise to energy relief due to the presence of free surface. We apply our result to the study of compositional and morphological instabilities of a stressed thin layer with a free surface. The critical wave number of instability is determined by the competition between the destabilizing influence of elastic strain energy and the stabilizing influence of chemical and surface energies.

The article proposes designing rectified piezoelectric power generators based on the direct finite element method. It accounts for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, and complicated structural configurations such as arrays of piezoelectric oscillators. The proposed model suggests replacing the energy harvesting circuit by an equivalent load impedance in series with negative piezoelectric capacitance. As the expression of the equivalent load impedance can be explicitly derived, the proposed finite element approach is capable of handling common interface circuits without resorting to circuit solvers. Finally, the model is extended to the consideration of SECE (synchronized electric charge extraction) circuit which offers an advantage of independence of harvested power on external loads.Copyright © 2014 by ASME

This article reports a novel finite element model of piezoelectric energy harvesters accounting for the effect of nonlinear interface circuits. The idea is to replace the energy harvesting circuit in parallel with the parasitic piezoelectric capacitance by an equivalent load impedance. This approach offers many advantages. First, the model itself can be implemented conveniently in commercial finite element softwares. Second, it directly provides system-level designs on the whole without resorting to circuit solvers. Third, the extensions to complicated structures such as array configurations are straightforward. The proposed finite element model is validated by considering the case of an array system endowed with the standard, parallel-/series-SSHI (synchronized switch harvesting on inductor) interfaces. Good agreement is found between simulation results and analytic estimates.