压电复合材料层合结构中的SH波

考虑压电耦合效应,通过传递矩阵-二维谱分析研究了压电复合材料层合板稳态SH波的频散特性和瞬态SH波的传播特性。数值分析表明: 压电耦合作用提高了SH波的截止频率和相速度; 由表面扰动激发的SH波, 一部分能量向板深度方向传播, 一部分以表面波的形式在两倍波长深度内传播。所采用的传递矩阵-二维谱分析为层合结构瞬态波动研究提供了一种有效的数值方法。      

Love waves propagation in a piezoelectric layered structure with initial stresses

Summary. The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.     

Love wave propagation in layered magneto-electro-elastic structures with initial stress

Summary An analytical approach is taken to investigate Love wave propagation in layered magneto-electro-elastic structures with initial stress, where a piezomagnetic (piezoelectric) material thin layer is bonded to a semi-infinite piezoelectric (piezomagnetic) substrate. The magneto-electrically open and short conditions are applied to solve the problem. The phase velocity of the Love wave is numerically calculated for the magneto-electrically open and short cases, respectively. The effect of the initial stress on the phase velocity and the magneto-electromechanical coupling factor are studied in detail for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. We find that the initial stress has an important effect on the Love wave propagation in layered piezomagnetic/piezoelectric structures.     

SH wave propagation in piezoelectric coupled plates

The propagation of shear horizontal (SH) wave in a piezoelectric coupled plate is investigated in this paper. Full account is taken of the piezoelectric coupling effect to the isotropic metal core in the mathematical model. One of the applications of this research is in the damage detection of the host metal structure from the wave propagation signal excited by the piezoelectric layer which is surface bonded on the surface of a metal core. This research is distinct from the previous works on SH propagation in piezoelectric structures because the piezoelectric materials were used as the core structure in the previous studies, and the potential of the studies was mainly on time-delay devices. The dispersive characteristics and the mode shapes of the transverse displacement and the electric potential of the piezoelectric layer are theoretically derived. The results from numerical simulations show that the phase velocity of the plate structure tends to the bulk shear wave velocity of the host metal core at high wave number when the shear wave velocity of host plate is larger than that of PZT bonded on it. Furthermore, there are three asymptotic solutions of wave propagation when the shear wave velocity of the host plate is smaller than that of PZT. The mode shape of the electric potential of the piezoelectric layer changes from the quadratic shape at lower wave number and with thinner piezoelectric layer to the shape with more zero nodes at higher wave number and with thicker piezoelectric layer. These findings are significant in the application of wave propagation in piezoelectric coupled structures     

Bulk wave propagation in layered piezomagnetic/piezoelectric plates with initial stresses or interface imperfections

Bulk wave propagation in laminated piezomagnetic/piezoelectric plates with initial stresses and imperfect interface is investigated using the state space approach. Either electrically and magnetically open or shorted conditions on the top and bottom surfaces are considered. The phase velocity and frequency spectra of the wave are numerically calculated for various electric and magnetic conditions, and normalized modes are also analyzed. Although numerical results do indicate that the initial compressive stress can reduce the phase velocity of the wave propagating in a layered multiferroic structure, the effect is not as obvious as that reported in literature where the initial stresses were taken far beyond the strength of real materials. While the imperfect interface affect the frequency spectra much greater than initial stresses, because imperfection decreases the structural stiffness.     

Modeling of wave propagation in layered piezoelectric media by a recursive asymptotic method

In this paper, a simple asymptotic method to compute wave propagation in a multilayered general anisotropic piezoelectric medium is discussed. The method is based on explicit second and higher order asymptotic representations of the transfer and stiffness matrices for a thin piezoelectric layer. Different orders of the asymptotic expansion are obtained using Padé approximation of the transfer matrix exponent. The total transfer and stiffness matrices for thick layers or multilayers are calculated with high precision by subdividing them into thin sublayers and combining recursively the thin layer transfer and stiffness matrices. The rate of convergence to the exact solution is the same for both transfer and stiffness matrices; however, it is shown that the growth rate of the round-off error with the number of recursive operations for the stiffness matrix is twice that for the transfer matrix; and the stiffness matrix method has better performance for a thick layer. To combine the advantages of both methods, a hybrid method which uses the transfer matrix for the thin layer and the stiffness matrix for the thick layer is proposed. It is shown that the hybrid method has the same stability as the stiffness matrix method and the same round-off error as the transfer matrix method. The method converges to the exact transfer/stiffness matrices essentially with the precision of the computer round-off error. To apply the method to a semispace substrate, the substrate was replaced by an artificial perfect matching layer. The computational results for such an equivalent system are identical with those for the actual system. In our computational experiments, we have found that the advantage of the asymptotic method is its simplicity and efficiency.     

Wave propagation in a thinly two layered laminated medium with stress couples under initial stresses

Summary The present paper is an attempt to provide an approximate treatment based on Biots theory of incremental deformation to study the wave propagation in two thinly layered laminated medium under initial stresses. The cross-sectional distortion which plays an important role in the coupling of adherent layers is taken into account. The theory is derived in the context of plane strain deformation and the frequency equation for phase velocity of waves propagated has been obtained. It has been shown that under certain conditions when wave length becomes small compared to thickness of each layer, the wave approaches to Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface.

Notation and Nomenclature

For Medium—I M _i, L_i elastic coefficients - C _i bending moment - h _i thickness - P _i initial stress - _i fraction of the total thickness occupied by theith layer - b _i couple-stress coefficient For the equivalent anisotropic continuum H total thickness - M, L elastic coefficients - P average initial stress - s ₁₁ ⁽¹⁾ ,s ₂₂,s ₁₂ ⁽¹⁾ incremental stress components - u ₁,v ₁ displacement components alongx, y directions respectively - ₁ density - e _xx,e _yy,e _xy ⁽¹⁾ strain components with respect to rotated axes - w ₁ rotational component aboutz-axis - f ₁ x, f ₁ y components of incremental boundary forces per unit initial area For Medium-II N _j,Q _j elastic coefficients - D _j bending moment - K _j thickness - R _j initial stress - _j fraction of the total thickness occupied by thejth layer - g _j couple-stress coefficients For the equivalent anisotropic continuum K total thickness - N, Q elastic coefficients - R average initial stress - s ₁₁ ⁽²⁾ ,s ₂₂,s ₁₂ ⁽²⁾ incremental stress components - u ₂,v ₂ displacement components alongx, y directions respectively - ₂ density - e _xx, e_yy,e _xy ⁽²⁾ strain components with respect to rotated axes - w ₂ rotational component aboutz-axis - f ₂ x, f ₂ y components of incremental boundary forces per unit initial area With 5 Figures     

Effects of the initial stress on the propagation and localization properties of Rayleigh waves in randomly disordered layered piezoelectric phononic crystals

In this paper, the effects of the initial stress on the propagation and localization properties of the Rayleigh surface waves in randomly disordered layered piezoelectric phononic crystals are studied. Due to different mechanical properties between the piezoelectric material and the polymer, different initial stresses in these two layers satisfying the equilibrium condition and interfacial compatibility are considered, which is more suitable for the practical cases. The transfer matrix between two consecutive piezoelectric unit cells is derived according to the continuity conditions. The expression of the localization factor is presented, and the wave localization properties are analyzed. Numerical calculations for the PVDF/PZT–2 periodic composites with the initial stress are performed. The band gap characteristics are studied taking the mechanical and electrical coupling into account. It is found that the localization degree can be influenced by the piezoelectric constants. With the increase in the piezoelectric constant, the stop band regions are enlarged for the ordered structures, and the localization properties of Rayleigh waves are strengthened for the disordered systems. The Rayleigh waves will be localized in mistuned periodic piezoelectric composites. The characteristics of band gaps and wave localization in ordered and disordered piezoelectric phononic crystals can be significantly changed by tuning the initial stress.     

Modeling of ultrasonic wave propagation in integrated piezoelectric structures under residual stress

The objective of this study is to understand the role of residual stress in piezoelectric layers in order to predict the performance of integrated structures. This is of particular importance in thick or thin film technology. Considering a bulk piezoelectric material, the Christoffel equation for a piezoelectric material is modified to take into account a uniform residual stress on a given cross section. A numerical study of its influence is carried out on the slowness curves and coupling coefficients of a lithium niobate material. In a second part, modified Christoffel tensor is used to calculate the dispersion curves of Lamb waves in a piezoelectric plate. The Lamb modes are found to be sensitive to the residual stress. In particular, it is shown how the behavior of the first Lamb modes is modified with residual stress. In a third part, these results are extended to a piezoelectric film laid down on a substrate in order to model the importance of these phenomena on the behavior of an integrated structure. The numerical study of guided waves in a lithium niobate plate is performed first, then the case of a lithium niobate film laid down on a silicon substrate is considered.     

Multi-modal wave propagation in smart structures with shunted piezoelectric patches

The propagation of wave modes in elastic structures with shunted piezoelectric patches is dealt with in this work. The wave finite element approach, which is based on the finite element method and periodical structure theory, is firstly developed as a prediction tool for wave propagation characteristics in beam like structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model (DMM). With these numerical techniques, reflection and transmission coefficients of propagating waves in structures with shunted piezoelectric patches can be calculated. The performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the DMM. Forced response of the smart structure can also be calculated, and based on which the time response of the structure can be obtained via an inverse discrete fourier transform approach. These general formulations can be applied to all types of slender structures. All these numerical tools can facilitate design modifications and systematic investigations of geometric and electric parameters of smart structures with shunted piezoelectric elements.     

粘性联结的层状固体媒质中兰姆波的传播

在复合材料中 ,当有粘弹体存在时 ,粘弹体的粘性会对波的传播造成一定影响。早期的 Thomson-Haskell矩阵以面波描述板层中的场 ,而面波的幅值在各个方向都是常数 ,因此它们不能描述在一衰减媒质中反射或透射波的衰减。本文中引入体波衰减的模型 ,即 Kelvin- Voigt的粘弹性描述 [1] ,该方法导致了一个复数波数。其实部描述了波的传播 ,而虚部则描述波的衰减。1　基本理论传递矩阵可以描述弹性波在包含任意多层的层状媒质中的传播特性 [2 ] 。1.1　无限弹性固体中的波对图 1所示的计算模型 ,其运动位移方程用矢量形式可表示为 :　　 ρ 2 U …     

Shear-horizontal surface waves in a layered structure of piezoelectric ceramics

A new existence condition for shear-horizontal (SH) surface waves in a layered structure of piezoelectric ceramics is give. The discussed SH surface wave is not a stiffened Love wave, but a new type surface wave.     

层状周期介质中的非线性平面声波的传播

对于在非线性媒质中传播的有限幅度平面波,可以一维拉格朗日坐标中的一维时空函数来表示;任一单频简谐波通常展开到二阶的形式:     

Crack propagation in ceramic composites with layered granular structure

Fracture experiments under conditions of subcritical crack extension were performed with double torsion and single-edge notched bend specimens of different alumina-based ceramic composites having layered granular structure. It is shown that it is possible to increase significantly the work-of-fracture as a result of layered granular structure organization. The pecularities of structure influence on the crack propagation kinetics were investigated, and the possibilities of acceleration and deceleration of subcritical crack growth are reported.     

SH-SAW propagation in layered functionally graded piezoelectric material structures loaded with viscous liquid

We investigate the properties of shear horizontal surface acoustic wave propagation in layered functionally graded piezoelectric material structures loaded with viscous liquid. The piezoelectric material is polarized in the z-direction and the material properties change gradually along the thickness of the layer. Interfacial mechanical conditions are continuity of particle velocity and stress components at the interface. We here assume that the liquid is electrically insulated and its permittivity is much less than that of the piezoelectric material. The solutions of dispersion relations are obtained for insulated liquid with electrically open or shorted conditions by means of transfer matrix method. The effects of the gradient variation of material constants on the phase velocity and attenuation are presented and discussed in detail. The analytical method and the results are useful for the design of the resonators and sensors.     

Acoustic wave propagation in piezoelectric fibers of hexagonalcrystal symmetry

An exact analysis is presented for acoustic wave propagation in cladded acoustic fibers having a core and an infinite thick cladding both made of piezoelectric hexagonal crystal of 6 mm point group symmetry. The crystalline Z axes of both the core and cladding coincide with the fiber axis. A general dispersion equation is derived for all the acoustic modes propagating along the fiber axis. Two simpler and independent equations which represent the dispersion relations of torsional and radial-axial modes can be separated from the general dispersion equation. It has been found that the radial-axial and general flexural modes are piezoelectrically active while the torsional modes are not. Approximate dispersion relations for pure guided modes in weakly guiding weakly piezoelectric fibers which are much simpler than the exact ones are also given. Numerical results are only presented for pure guided modes. Exact and approximate dispersion curves of several lower order pure guided flexural, radial-axial and torsional modes in a weakly guiding ZnS fiber are compared and they are in good agreement     

Dispersion relations for SH-wave propagation in periodic piezoelectric composite layered structures

Propagation behavior of horizontally polarized shear waves (SH-waves) in a periodic piezoelectric-polymeric layered structure is taken into account. The layered structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the periodic layered piezoelectric structure are obtained for the cases of wave propagation in the direction normal to the interface and along the interface, respectively. Filter effect of this kind of structure and the effects of volume fraction and shear modulus ratio of piezoelectric layer to polymeric layer on the phase velocity are discussed in detail, respectively. One set of piezoelectric thin film--polymeric thin film multilayer system (PZT-5H piezoelectric ceramics--polythene) is chosen to show the numerical simulation, basic properties of SH-waves propagation in this particular structure are revealed.     

Finite-element simulation of wave propagation in periodic piezoelectric SAW structures

Many surface acoustic wave (SAW) devices consist of quasiperiodic structures that are designed by successive repetition of a base cell. The precise numerical simulation of such devices, including all physical effects, is currently beyond the capacity of high-end computation. Therefore, we have to restrict the numerical analysis to the periodic substructure. By using the finite-element method (FEM), this can be done by introducing periodic boundary conditions (PBCs) at special artificial boundaries. To be able to describe the complete dispersion behavior of waves, including damping effects, the PBC has to be able to model each mode that can be excited within the periodic structure. Therefore, the condition used for the PBCs must hold for each phase and amplitude difference existing at periodic boundaries. Based on the Floquet theorem, our two newly developed PBC algorithms allow the calculation of both, the phase and the amplitude coefficients of the wave. In the first part of this paper we describe the basic theory of the PBCs. Based on the FEM, we develop two different methods that deliver the same results but have totally different numerical properties and, therefore, allow the use of problem-adapted solvers. Further on, we show how to compute the charge distribution of periodic SAW structures with the aid of the new PBCs. In the second part, we compare the measured and simulated dispersion behavior of waves propagating on periodic SAW structures for two different piezoelectric substrates. Then we compare measured and simulated input admittances of structures similar to SAW resonators.