Nonlinear dynamic responses of a truss core sandwich plate

Nonlinear dynamic behaviors of a simply supported 3D-Kagome truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in this paper. The truss core sandwich plate is equivalent to a laminated plate with three laminas according to the equivalent sandwich plate method. The governing equation of motion for the truss core sandwich plate is derived by using the von Karman type equation for the geometric nonlinearity and the Reddy’s third-order shear deformation plate theory. The nonlinear governing partial differential equation is reduced to the ordinary differential equation by applying the Galerkin’s approach. The four-dimensional averaged equation is obtained by using the method of multiple scales. The frequency–response curves are obtained under consideration of strongly coupled of two modes. The results indicate that there are the hardening and softening nonlinearities in the truss core sandwich plate under the specific resonant case. The influences of the amplitudes for the in-plane and transverse excitations on the frequency–response curves are investigated. The results of numerical simulations for the two-degree-of-freedom nonlinear equation exhibit the existence of the period, multi-period and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.