Wave localization in randomly disordered periodic layered piezoelectric structures

Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.

PROPAGATION OF SURFACE ACOUSTIC WAVES IN PRESTRESSED ANISOTROPIC LAYERED PIEZOELECTRIC STRUCTURES

The propagation of surface acoustic waves in layered piezoelectric structureswith initial stresses is investigated. The phase velocity equations are obtained for electricallyfree and shorted cases, respectively. Effects of the initial stresses on the phase velocity and theelectromechanical coupling coefficient for the fundamental mode of the layered piezoelectricstructures are discussed. Numerical results for the c-axis oriented film of LiNbO_3 on a sapphiresubstrate are given. It is found that the fractional change in phase velocity is a linear functionwith the initial stresses, and the electromechanical coupling factor increases with an increase ofthe absolute values of the compressive initial stresses. The results are useful for the design ofsurface acoustic wave devices.

Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions

Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics.During the past few decades,the method of fundamental solutions(MFS)has emerged as a popular and well-established meshless boundary collocation method for the numerical solution of many engineering applications.The classical MFS formulation,however,leads to dense and non-symmetric coefficient matrices which will be computationally expensive for large-scale engineering simulations.In this paper,a localized version of the MFS(LMFS)is devised for electroelastic analysis of twodimensional(2D)piezoelectric structures.In the LMFS,the entire computational domain is divided into a set of overlapping small sub-domains where the MFS-based approximation and the moving least square(MLS)technique are employed.Different to the classical MFS,the LMFS will produce banded and sparse coefficient matrices which makes the method very attractive for large-scale simulations.Preliminary numerical experiments illustrate that the present LMFM is very promising for coupled electroelastic analysis of piezoelectric materials.

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.

A three-layer structure model for the effect of a soft middle layer on Love waves propagating in layered piezoelectric systems

A three-layer structure model is proposed for investigating the effect of a soft elastic middle layer on the propagation behavior of Love waves in piezoelectric layered systems, with ＂soft＂ implying that the bulk-shear-wave velocity of the middle layer is smaller than that of the upper sensitive layer. Dispersion equations are obtained for unelectroded and traction-free upper surfaces which, in the limit, can be reduced to those for classical Love waves. Systematic parametric studies are subsequently carried out to quantify the effects of the soft middle layer upon Love wave propagation, including its thickness, mass density, dielectric constant and elastic coefficient. It is demonstrated that whilst the thickness and elastic coefficient of the middle layer affect significantly Love wave propagation, its mass density and dielectric constant have negligible influence. On condition that both the thickness and elastic coefficient of the middle layer are vanishingly small so that it degenerates into an imperfectly bonded interface, the three-layer model is also employed to investigate the influence of imperfect interfaces on Love waves propagating in piezoelectric layer/elastic sub- strate systems. Upon comparing with the predictions ob- tained by employing the traditional shear-lag model, the present three-layer structure model is found to be more ac- curate as it avoids the unrealistic displacement discontinuity across imperfectly bonded interfaces assumed by the shearlag model, especially for long waves when the piezoelectric layer is relatively thin.

STRESS ANALYSIS AND GEOMETRICAL CONFIGURATION SELECTION FOR MULTILAYER PIEZOELECTRIC DISPLACEMENT ACTUATOR

Multilayer piezoelectric ceramic displacement actuators are susceptible to cracking in the region near the edge of the internal electrode, which may cause system damage or failure. In this paper, the stress distribution of a multilayer piezoelectric composite is investigated in a working environment and the optimized geometrical con?guration of the piezoelectric layer is obtained. The stress distribution in the structure and the stress concentration near the edge of the internal electrode, induced by non-uniform electric ?eld distribution, are analyzed by moir′e interferometry experiment and ?nite element numerical simulation. Based on the above analysis, two optimized geometrical models are presented for the purpose of geometrical con?guration selection, with which stress concentration can be reduced signi?cantly while the feasibility of the machining process and the basic structural functions occurring in the conventional model are retained. The numerical results indicate that the maximum stress in the optimized models is e?ectively diminished compared to the conventional model. For instance, the peak value of the principal stress in the optimized model II is 93.1% smaller than that in the conventional model. It is proved that stress concentration can be e?ectively relaxed in the latter of the two optimized models and thus the probability of fracture damage can be decreased.

A wavelet approach for active-passive vibration control of laminated plates

As an extension of the wavelet approach to vi- bration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid active- passive control strategy for suppressing vibrations of lami- nated rectangular plates bonded with distributed piezoelec- tric sensors and actuators via thin viscoelastic bonding lay- ers. Owing to the low-pass filtering property of scaling func- tion transform in orthogonal wavelet theory, this wavelet- based control method has the ability to automatically filter out noise-like signal in the feedback control loop, hence re- ducing the risk of residual coupling effects which are usu- ally the source of spillover instability. Moreover, the exis- tence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process. A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control pro- cess. Numerical results demonstrate the efficiency of the pro- posed approach.

Size-dependent vibrations and waves in piezoelectric nanostructures:a literature review

With the development and applications of nano-electro-mechanical systems,academic interest in the mechanical behavior of piezo-electric structures at nanoscale is increasing.Interesting unconven-tional phenomena have been observed either experimentally or through molecular dynamics simulation.The most common and also important one is the size-dependent characteristics.Classical continuum mechanics with necessary modifications has been pro-ven to be very powerful in explaining these particular characteris-tics in a relatively simple theoretical framework.This article reviews the recent advances in understanding the size-dependent dynamic responses of piezoelectric nanostructures from the viewpoint of modified continuum mechanics.Particular attentions are paid to three advanced theories of piezoelectricity(e.g.gradient piezoelec-tricity,surface piezoelectricity,and nonlocal piezoelectricity)and their abilities to predict unconventional vibration and wave char-acteristics in piezoelectric structures and devices at the nanoscale.The article could serve as a useful reference for the future research on or design of nanostructures with multifield couplings.

Peculiarities of surface acoustic waves,propagation in structures with functionally graded piezoelectric materials,coating from different ceramics on the basis of PZT

A model of a piezoelectric structure with an inhomogeneous coating is considered.The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating.The properties of coating vary continuously in thickness from parameters of one material to parameters of another material in a continuously nonmonotonic or piecewise-continuous manner.As coating materials,various combinations of ceramics of different stiffness based on PZT are considered.Using the example of the problem of the propagation of sh-waves in a piezoelectric structure,we studied the influence of the ratio of the physical parameters of the coating materials,the localization region,and the size of the transition zone of one material to another on the propagation features of surface acoustic waves(SAWs)and the structure of the wave field.

Static Force Reliability Analysis of Truss Structure with Piezoelectric Patches Affixed to Its Surface

For the truss structure composed of active-elements with piezoelectric patches affixed to its surface,taking the mechani-cal-electric coupling effect under the action of electric loads and mechanical loads into consideration,the finite element model for static force analysis is established by using the theory of mechanics. The failure mechanism of piezoelectric elements is discussed and the failure criteria of piezoelectric elements are proposed. The expression of safety margins for the element of piezoelec...

Specific features of SH-waves propagation in structures with prestressed inhomogeneous coating made of piezoceramics based on LiNbO_(3)

Within the framework of the linearized theory of electroelastic wave propagation,a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered.The ferroelectric LiNbO_(3) is used as the main material of the structure.The initial deformed state of the coating material is homogeneous,induced by the action of initial mechanical stresses and an external electrostatic field,the properties of the coating continuously change in thickness.By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface,the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied.The separate and combined effects of initial actions on changes in the physical properties of the structure,the transformation of the surface wave field,and the change in the SAW velocities in a wide frequency range is studied.The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures,in the optimization and design of new structures and devices on SAW with high performance characteristics.

Band gap structure analysis of phononic crystal rods with hybrid shunted piezoelectric patches

The band gap structures by arranging hybrid shunted piezoelectric materialswith resistance inductive （RL） circuit and negative impedance converter （NIC） closely and at in- tervals are presented. The theoretical model is built using transfer matrix method. Then the MATLAB computing language is utilized to simulate the band gap structures. Meanwhile, the effects of the resistance, inductance and capacitance on the local resonant gap are studied. By comparing different combinations of resistance, inductance and capacitance as well as different arrangement of circuits, a 13 kHz band gap is reached under the effect of arranging hybrid pe- riodic shunted piezoelectric patches at intervals and the stability of the system is also analyzed. It is proved that utilizing hybrid shunted piezoelectric patches would have a clear impact on the band gap structure of phononic crystal rods. Moreover, the band gap would be clearly enlarged by arranging hybrid piezoelectric patches at intervals.

Composition dependence of phase structure and electrical properties of(1-y)Bi_(1-x)Nd_xFeO_(3-y)BiScO_3 ceramics

In this work, we have studied a new lead-free ceramic of（1-y）Bi1-xNdxFeO3-yBiScO3（0.05≤x≤0.15 and 0.05≤y≤0.15） prepared by a conventional solid-state method, and the influences of Nd and Sc content on their phase structure and electrical properties were investigated in detail. The ceramics with 0.05≤x≤0.10 and 0.05≤y≤0.15 belong to an R3 c phase, and the rhombohedral-like and orthorhombic multiphase coexistence is established in the composition range of 0.125≤x≤0.15 and y=0. The electrical properties of the ceramics can be enhanced by modifying x and y values. The highest piezoelectric coefficient（d33～51 p C/N） is obtained in the ceramics with x=0.075 and y=0.125, which is superior to that of a pure BiFeO3 ceramic. In addition, a lowest dielectric loss（tan δ～0.095%, f=100 k Hz） is shown in the ceramics with x=0.15 and y=0 due to the involvement of low defect concentrations, and the improved thermal stability of piezoelectricity at 20–600℃ is possessed in the ceramics. We believe that the ceramics can play a meaningful role in the high-temperature lead-free piezoelectric applications.