Nonlinear dynamic response of a sandwich structure with flexible core in thermal environments

Nonlinear dynamic response with stability analysis of a sandwich structure with flexible core are investigated by integration of variational asymptotic method (VAM) and the first-order shear deformation theory. A simply supported sandwich structure is subjected to an harmonic transverse excitation in thermal environments. Generalized 2 D Reissner-Mindlin type stiffness matrices including an equivalent transverse shear matrix are obtained based on through-the-thickness analysis using VAM without invoking any ad hoc kinematic assumptions. The governing equation is derived using Hamilton's principle taking into account von Ka ' rma ' n geometric nonlinearity. Galerkin's method is employed to develop a nonlinear differential equation of the problem with quadratic and cubic nonlinearities, which are associated with the coupling of the in-plane stretching and transverse deflection due to thermal moments. Periodic solutions are determined using the incremental harmonic balance (IHB) method and incremental arc-length technique. The stability is evaluated by Routh-Hurwitz theory. The effects of the temperature variation, geometric parameters and material properties on the resonance as well as amplitude of steady state vibration are investigated through a detail parametric study.