The Computation of Complex Dispersion and Properties of Evanescent Lamb Wave in Functionally Graded Piezoelectric-Piezomagnetic Plates

Abstract

Functionally graded piezoelectric-piezomagnetic material (FGPPM), with a gradual variation of the material properties in the desired direction(s), can improve the conversion of energy among mechanical, electric, and magnetic fields. Full dispersion relations and wave mode shapes are vital to understanding dynamic behaviors of structures made of FGPPM. In this paper, an analytic method based on polynomial expansions is proposed to investigate the complex-valued dispersion and the evanescent Lamb wave in FGPPM plates. Comparisons with other related studies are conducted to validate the correctness of the presented method. Characteristics of the guided wave, including propagating modes and evanescent modes, in various FGPPM plates are studied, and three-dimensional full dispersion and attenuation curves are plotted to gain a deeper insight into the nature of the evanescent wave. The influences of the gradient variation on the dispersion and the magneto-electromechanical coupling factor are illustrated. The displacement amplitude and electric potential and magnetic potential distributions are also discussed in detail. The obtained numerical results could be useful to design and optimize different sensors and transducers made of smart piezoelectric and piezomagnetic materials with high performance by adjusting the gradient property.

Experimental Analysis of Welded Rods with a Functionally Graded Material Approach

“…It should be noted that, there are many other studies related to FGM in the literature [36][37][38]. There are many theoretical examples of the thermal behavior and mechanical analysis (vibration, wave propagation, bending and buckling) of axially FGM in the literature [39][40][41][42][43]. The purpose of this study is to establish a link between theoretical and experimental studies.…”

Guided waves propagation in arbitrarily stacked composite laminates: Between-layers incompatibility issue resolution using hybrid matrix strategy

“…The remaining numerical methods available from the literature are the higher order plate theory method (HOPT) [41][42][43], Legendre polynomial method (LPM) [44][45][46], Ritz-Rayleigh method [47,48], Green's function [49], and Green's matrix method [50]. These methods keep the approximation property that at larger frequency range or for the higher order modes, they generally produce a poor accuracy of solutions.…”

The Experimental Registration of the Evanescent Acoustic Wave in YX LiNbO3 Plate

“…In the case of a purely imaginary wavenumber or with a significant excess of the imaginary part relative to the real part, the evanescent mode corresponds to vibration near the source of the external force, which decays exponentially with the distance from the source and does not transfer energy [ 1 , 2 , 3 , 4 ]. The theoretical studies of the dispersion dependences of such waves propagated in isotropic plates [ 1 , 2 , 3 , 4 ], piezoelectric plates of cubic symmetry [ 5 ], functionally graded piezoelectric-piezomagnetic plates [ 6 ], phononic crystals [ 7 ] were carried out earlier. These studies were carried out for non-dissipative media with zero viscosity.…”