Guided wave propagation in multilayered piezoelectric structures

Abstract

A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures. multilayered piezoelectric structures, the method of reverberation-ray matrix, guided waves, dispersion characteristic Piezoelectric materials have been applied in many important fields such as geophysics, electronics, communication, instrumentation and nondestructive evaluation and testing of materials [1] . Numerous ultrasonic devices, based on either surface acoustic wave (SAW) or bulk acoustic wave (BAW), have been developed using piezoelectric materials for a variety of applications [2,3] . These devices are usually fabricated with a layered geometry, because of its high sensitivity, great bandwidth, and enhanced reception characteristics [4][5][6][7][8][9][10][11] . Currently, in order to satisfy the increasing demand of higher frequency, higher performance, smaller size, lower cost and lower energy consumption, thin film piezoelectric stack structures are widely used with the maturation of thin film technologies. Thin film bulk acoustic resonator (TFBAR) and solidly mounted resonator (SMR) are two typical examples [12][13][14] . For the sake of design and optimization, appropriate theoretical models and efficient solution methods are desired to investigate the behaviors of wave propagation in these devices. It is common to use layered model consisting of piezoelectric and non-piezoelectric layers stacked in a certain sequence for these piezoelectric devices [4][5][6][7][8][9][10][11][12][13] . So far, various matrix analysis methods have been proposed in the study of wave propagation in multilayered piezoelectric structures [1][2][3][4][5][6][7][8][9][10][11][12][15][16][17][18][19][20][21][22][23][24][25][26][27] , such as the finite element method (FEM) [4,10] , the transfer matrix method (TMM) [1][2][3]15,16] , the scattering-matrix method [8] , the surface impedance

Reverberation-Ray Matrix Analysis of Acoustic Waves in Multilayered Anisotropic Structures

“…where the global arriving and departing wave vectors a and d are Tian et al, 2006), which guarantees the numerical stability and at the same time enables the inclusion of surface and interface wave modes, in the proposed formulation of MRRM (Guo & Chen, 2008a, 2008bGuo, 2008;Guo et al, 2009). (18) and (19), Eqs.…”

“…Thus, it can give more accurate results but at less computational expense especially in the high-frequency range. Recently, the characteristics of free waves in single PZT-4 and/or barium sodium niobate (BSN) layers have been discussed (Guo et al, 2009) for different boundary conditions, and dispersion curves of bi-layered, triple-layered and ten-layered piezoelectric structures composed of alternate PZT-4 and BSN layers with equal thickness were also presented (Guo & Chen, 2008b;Guo et al, 2009). Here in this chapter, a four-layered composite with a 0°/90°/0°/90° configuration is considered.…”

Precise Analysis and Design of Multi-Layered Acoustic Wave Devices with Bragg Cell

“…It should be noted that the above proposed formulation of MRRM (Guo & Chen, 2008a, 2008bGuo, 2008;Guo et al, 2009) excludes any exponentially growing function and matrix inversion, therefore possesses unconditionally numerical stability and enables inclusion of surface and interface wave modes.…”

“…Tan (2007) compared most analytical methods in their mathematical algorithm, computational efficiency and numerical stability. Very recently, Guo et al (Guo, 2008;Guo & Chen, 2008a, 2010Guo et al, 2009) have presented a new version of the analytical method of reverberation-ray matrix (MRRM) formerly proposed by Pao et al (Su et al, 2002;Pao et al, 2007), based on three-dimensional elasticity/ piezoelectricity (Ding & Chen, 2001), state-space formalism (Stroh, 1962) and plane wave expansion for the analysis of free waves in multi-layered anisotropic structures. The new formulation of MRRM deals with the exponentially growing and decaying terms separately and refrains from matrix inversion.…”

Modelling guided waves in anisotropic plates using the Legendre polynomial method

“…There are many methods to investigate the propagation characteristics of guided waves in composite laminates. These method include the Transfer matrix method (TMM) [3,4], the Global matrix method (GMM) [5], the scattering matrix method(SMM) [6], the stiffness transfer matrix method(STMM) [1], reverberation-ray matrix method(RMMM) [7,8], the finite element method (FEM) [9][10][11], and the semi-analysis finite element method (SAFE) [12]. Guided waves propagation can then be found by imposing appropriate boundary.…”