A semi‐analytical framework for time history response of a carbon nanotube‐reinforced polymer damped composite plate: Influence of instability regions

Abstract The influence of dynamic instability regions (DIRs) (stable and unstable) on the time history response of a randomly distributed carbon nanotube‐reinforced polymer composite (RD‐CNTRPC) plate under partial edge (nonuniform) in‐plane loading is presented semi‐analytically in this study. Kinematics of the RD‐CNTRPC plate is expressed based on higher‐order shear deformation theory (HSDT) and includes von‐Kármán nonlinearity. The effective isotropic mechanical properties of the RD‐CNTRPC plate (CNT mixed with epoxy) are executed using the Eshelby‐Mori‐Tanaka technique. The prebuckling stresses generated within the plate due to the partial‐edge in‐plane loading is computed using Airy's stress approach. The computed pre‐buckling stresses are used while applying Hamilton's principle to develop the governing nonlinear partial differential equation (PDEs). The PDEs are solved via. Galerkin's method to convert into the nonlinear ordinary differential equations (ODEs). These ODEs are solved using Newmark's method to trace the time history responses of the RD‐CNTRPC plate. The boundaries of DIRs are estimated using Bolotin's method. The effect of frequencies corresponding to upper, lower, and unstable regions of DIRs on the time history response and phase plot of the RD‐CNTRPC plate with and without damping are examined in detail.