Semianalytical Development of Dynamic Instability and Response of a Multiscale Laminated Hybrid Composite Plate

Abstract

The use of carbon nanotubes (CNTs) in augmenting the mechanical properties of fiber-reinforced laminated composites is a fact. In this paper, the semianalytical studies on the dynamic instability behavior and linear and nonlinear responses of a randomly distributed CNT and fiber-reinforced interlamina hybrid composite (CNTFRHC) plate with and without damping under time-dependent in-plane uniaxial uniform compression loading are presented. Each lamina of the laminate is made of multiscale materials such as CNT/polymer/fiber. The effective mechanical properties of the lamina are estimated in two steps. First, the Eshelby–Mori–Tanaka technique is used to compute the effective mechanical properties of randomly distributed CNTs in a polymer matrix (i.e., CNT-embedded matrix). Second, the effective mechanical properties of the CNT-embedded matrix reinforced with fiber (either carbon or glass) are estimated by using various homogenization techniques. The plate is modeled by using higher-order shear deformation theory (HSDT) and von Kármán nonlinearity. Governing partial differential equations of the CNTFRHC plate are obtained by Hamilton’s principle and reduced to Mathieu–Hill equations by using the Galerkin method. Mathieu–Hill equations are solved by the Bolotin method to trace the boundaries of the instability region corresponding periods T and 2T. Finally, the influence of different parameters such as CNT agglomerations, CNT mass fraction, edge-to-thickness ratio, compression preloading, boundary conditions, and damping on the dynamic instability region of the CNTFRHC plates are studied in detail. Numerical results provide useful insights into the selection of parameters with different combinations for the desired design of the CNTFRHC plate against instability. Furthermore, to know the characteristics of the instability region of a CNTFRHC plate such as the existence of beats, dependence on geometric nonlinearity, and forcing frequency for which the linear and nonlinear responses with and without damping in both stable and unstable regions are presented.