Guided wave characteristics in functionally graded piezoelectric rings with rectangular cross-sections

Abstract

For the purpose of design and optimization of functionally graded piezoelectric material (FGPM) transducers, wave propagation in FGPM structures has received much attention in the past twenty years. But previous research efforts have been focused essentially on semi-infinite structures and one-dimensional 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 solving the wave propagation problem in a two-dimensional FGPM structure, namely an FGPM ring with a rectangular cross-section. By numerical comparison with the available reference results for a purely elastic homogeneous rectangular rod, the validity of the extended polynomial approach is illustrated. The dispersion curves and the electric potential distributions of various FGPM rectangular rings with different material gradient directions, different polarization directions, different radius to thickness ratios, and different width to thickness ratios are calculated to reveal the guided wave characteristics

Analysis of wave propagation in cylinders and rods made of functionally graded piezoelectric material

“…In the numerical examples given below two types of piezoelectric materials are considered: PZT-4 and LiNbO3. The corresponding material parameters are given in Table 1 [4]. We consider the piezoelectric transducers of the shape described in the preceding section and assume their surfaces are insulated.…”

“…Many computational methods have been developed to solve the wave propagation in complex FGPM structures. In [4] an approach based on double orthogonal polynomial series for solving the wave propagation problem in a two-dimensional FGPM structure, which is FGPM ring with a rectangular cross-section, is proposed. Effects of various physical parameters on dispersion curves and cutoff frequencies in a Y-cut quartz plate with elastic or functionally graded top layer are studied in [5].…”

Full dispersion and characteristics of complex guided waves in functionally graded piezoelectric plates

“…At fixed values of real k, equation ( 13) is a positive-definite generalized eigenvalue problem with real positive roots v 2 . If interest is the propagating wave, then it is very efficient to specify real k and then solve for v. In the previous researches (Yu et al, 2009(Yu et al, , 2015Othmani et al, 2017), the dispersion relation is transformed a classical eigenvalue problem in v, which is relatively easy to be solved. But for the evanescent wave, the simple approach is not useful because wave number k is complex and the solving of equation ( 13) becomes much more complicated.…”

“…Using the spectral element method, Chakraborty et al (2005) characterized the wave propagation in FGPM plates by the thin-layer model. Yu et al (2009Yu et al ( , 2015 investigated the wave characteristics in FGPM hollow cylinders and FGMP rings with rectangular crosssections using the Legendre polynomial series expansion approach. Wu and Tsai (2012) developed a modified Pagano method for the three-dimensional (3D) static analysis of FGPM sandwich cylinders under electromechanical loads.…”

Computation of dispersion relations of functionally graded rectangular bars

“…Lefebvre [11] developed the Legendre orthogonal polynomial series expansion approach to investigate the acoustic wave propagation in the FGM cylinder. Yu [12][13][14] extended this method to analyze the dispersive behavior on wave propagation in magneto-electro-elastic hollow cylinders and piezoelectric rings with rectangular cross-sections of FGM and proposed an extended orthogonal polynomial approach to study propagation characteristics of the axial wave in layered piezoelectric rectangular bar. However, the dissymmetric eigenmatrix obtained by this approach is disadvantage of the solution of the dispersion curves.…”