Wave propagation analysis of Micropolar-Cosserat periodic composite panels: spectral element formulation

This research proposes the analytical model of wave propagation through a Micropolar-Cosserat (MC) periodic composite panel (PCP). A periodic panel comprises a transversely isotropic lamina that lies in the anisotropic domain material. The micro-mechanics of the lamina approach is adopted to obtain the equivalent stresses from the fiber-matrix constituents. Rodrigues’s rotation transformation matrix formula converts the local stresses into global ones. The coefficient matrix for the one-dimensional (1-D) linear composite model is derived from the state-space approach. The concept of compatibility equation is applied to the panels to design the unit cell of a periodic structure. The propagation constant in the eigenvalue domain is obtained using Bloch–Floquet’s theorem on the unit cell, which accounts for periodicity. A detailed transfer matrix formulation is developed to determine the wave propagation characteristics of the PCP. Next, the dynamic stiffness (DS) matrix for a finite structure made up of seven-unit cells is assembled using the spectral element (SE) formulation to examine the frequency response function (FRF). The formulation of the SE matrix for the plane-stress (PS) analysis is a significant advance in investigating the dynamic characteristics such as band-gap (BG) and FRF of the proposed structure. The BG and FRF obtained from the 1-D MC analysis and 1-D PS analysis are well corroborated with the finite element model (FEM). The validation will allow for further studies on various orientations of the lamina.