Impact of Micromechanical Approaches on Wave Propagation of FG Plates via Indeterminate Integral Variables with a Hyperbolic Secant Shear Model

Abstract

The aim of this paper is to analyze the impacts of micromechanical approaches on the wave propagation of a functionally graded (FG) plate via indeterminate integral variables with hyperbolic secant shear displacement models. This model is established based on a high-order theory and a new displacement field with four unknowns introducing indeterminate integral variables with a secant hyperbolic shear function. Six micromechanical approaches are applied to approximate the effective material properties of an FG plate, namely Voigt’s model, Reuss’ model, Hashin–Shtrikman’s lower, and upper bound models, Tamura’s model, and the LRVE model. The volume fractions are supposed to change corresponding to the power-law and sigmoid. By applying Hamilton’s principle, general formulae of the wave propagation were obtained to get the wave modes and phase velocity curves of wave propagation in FG plates, with the impact of Voigt’s, Reuss’, Hashin–Shtrikman’s bounds, Tamura’s, and LRVE explicit micromechanical models.

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

“…Besides, Bouazza et al studied the thermoelastic buckling behavior of functionally graded rectangular plates [54][55][56][57][58] and the Laminated Beams [59,60] based on hyperbolic shear deformation theory. And then, Bouazza et al studied hygro-thermo-mechanical buckling of laminated plates [61,62] and beam [63] and analyzed the impacts of micromechanical approaches on the wave propagation in a functionally graded plate [64].…”