Anti-Plane Wave Propagation in the Functionally Graded Hybrid Structure under an External Impulsive Force: A Green’s Function Approach

Abstract

To propagate the anti-plane wave, a hybrid layered-half-space schematic of fiber-reinforced and orthotropic materials is taken into account. Due to its importance in engineering applications, anti-plane wave propagation through functionally graded orthotropic materials has attracted a lot of attention. The functionally graded orthotropic materials in the half-space and the reinforced materials under high initial stress are utilized in the superficial layer of finite depth. To examine the effect of heterogeneity on wave phase velocity, the elastic characteristics of orthotropic materials are defined in terms of hyperbolic functions. Moreover, a rectangular plate is installed at the interface of the materials to expose the effect of irregularity in the materials. An external force (impulsive force) is applied to the wave at the point source of the disturbance to understand the influence of such a force on the phase velocity of the wave. The nonhomogeneous equations of motion are deduced by Fourier transformation and are solved analytically by Green’s function technique along with possible applications of Dirac delta function. The dispersion relation of the anti-plane wave propagation is obtained analytically. This study presents a graphic explanation of the proposed schematic and discusses the stability of the model.