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.
Highlights
Due to the excellent coupling behavior among mechanical, electric, and magnetic fields, piezoelectric-piezomagnetic composites composed of piezoelectric and piezomagnetic phases have been increasingly applied to different engineering structures, especially to the smart or intelligent systems as intelligent sensors, damage detectors, etc. [1]
Based on the previous formulations, the computer program in terms of the presented method has been written using Mathematica software to calculate the dispersion and phase velocity curves for the Functionally graded piezoelectric-piezomagnetic material (FGPPM) plate composed of CoFe2 O4 and Ba2 TiO3, h = 1 mm
The results show that the effect of the graded field on dispersion characteristics of Lamb wave is significant, including the propagating modes and evanescent modes
Summary
Due to the excellent coupling behavior among mechanical, electric, and magnetic fields, piezoelectric-piezomagnetic composites (or magneto-electro-elastic material) composed of piezoelectric and piezomagnetic phases have been increasingly applied to different engineering structures, especially to the smart or intelligent systems as intelligent sensors, damage detectors, etc. [1]. Materials 2018, 11, 1186 presented the differential equations governing the transfer and stiffness matrices for a functionally graded generally anisotropic magneto-electro-elastic medium and calculated the surface wave velocity dispersion. Wu et al [11] investigated the wave propagating characteristics in the non-homogeneous magneto-electro-elastic plates by using orthogonal polynomial approach. Xiao et al [14] investigated the dispersion properties of wave propagation in the functionally graded magneto-electro-elastic plate by the Chebyshev spectral element method. Studies on the guided wave in FGPPM structures are limited to the propagating waves, but the evanescent waves have not been investigated. Chen et al [24] studied theoretically the real-valued and imaginary-valued SH waves in a piezoelectric plate of cubic crystals These researches focused on the simple material and purely imaginary modes. The displacement amplitude and electric potential and magnetic potential distributions are discussed in detail
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