A technique for modelling multiple piezoelectric layers

Cai, Chao; Liu, G R; Lam, K.Y.

doi:10.1088/0964-1726/10/4/312

Cited by 26 publications

(7 citation statements)

References 22 publications

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“…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 matrix method [9,17,18] , the compound matrix method [19] , the recursive compliance/stiffness matrix method …”

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confidence: 99%

Guided wave propagation in multilayered piezoelectric structures

Guo

Chen

Zhang

2009

Sci. China Ser. G-Phys. Mech. Astron.

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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

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confidence: 99%

Guided wave propagation in multilayered piezoelectric structures

Guo

Chen

Zhang

2009

Sci. China Ser. G-Phys. Mech. Astron.

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“…The transfer matrix method has been applied for designing some acoustic structures, especially layered structures and simulating or analysing the propagation of sound waves within such structures. 23,24 For the constant cross section, the transfer matrix is given as follows: 25…”

Section: Design Proceduresmentioning

confidence: 99%

Design of Ultrasonic Transducer for Secondary Wave Generations with High Directivity

Kim¹,

Kim²,

Ri³

2019

The International Journal of Acoustics and Vibration

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In this paper, we described a method of designing ultrasonic transducer which simultaneously radiates two finite-amplitude ultrasonic waves to produce the secondary waves with high directivity. For nonlinear effects, it is necessary that the frequencies of two primary waves are coincident with natural frequencies of the ultrasonic transducer. The main problem here is to predict the resonance frequencies of the first mode as well as higher modes. While the first resonance frequency of the transducer can be estimated easily, it is not trivial to do higher ones. When the length of transducer is much greater than its diameter, this problem is reduced to one-dimensional and higher mode frequencies are nothing but multiples of the first mode frequency. However, such a case is seldom encountered. Using the transfer matrix method, we obtained the resonance frequencies of the transducer analytically and compared these with numerical results from the simulation. The theoretical and simulation results are in good agreement with the difference of 3--6 kHz.

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“…Many solution methods have been used to investigate the wave propagation phenomena in multilayered piezoelectric structures. The mostly used method is the transfer matrix method (TMM) [Nayfeh 1995;Adler 2000;Cai et al 2001] and the finite element method (FEM) [Ballandras et al 2004]. Because the TMM and FEM suffer from numerical instability in some particular cases, some improvements have been developed, such as the recursive asymptotic stiffness matrix method [Wang and Rokhlin 2002;, the surface impedance matrix method [Collet 2004;Zhang et al 2001], the scattering-matrix method [Pastureaud et al 2002] and the reverberation-ray matrix method [Guo et al 2009].…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in layered piezoelectric rings with rectangular cross sections

Yang

Lefebvre

2016

J. Mech. Mater. Struct.

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Wave propagation in multilayered piezoelectric structures has received much attention in past forty years. But the research objects of previous research works are almost only for semi-infinite structures and onedimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes a double orthogonal polynomial series approach to solve the wave propagation in a two-dimensional (2-D) layered piezoelectric structure, namely, a multilayered piezoelectric ring with a rectangular cross-section. Through numerical comparison with the available reference results for a purely elastic multilayered rectangular straight bar, the validity of the double polynomial series approach is illustrated. The dispersion curves and electric potential distributions of various layered piezoelectric rectangular rings with different material stacking directions, different polarization directions, different radius to thickness ratios, and different width to thickness ratios are calculated to reveal their wave propagation characteristics.

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A technique for modelling multiple piezoelectric layers

Cited by 26 publications

References 22 publications

Guided wave propagation in multilayered piezoelectric structures

Guided wave propagation in multilayered piezoelectric structures

Design of Ultrasonic Transducer for Secondary Wave Generations with High Directivity

Wave propagation in layered piezoelectric rings with rectangular cross sections

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