Nonlinear primary resonance with 1:3:6 internal resonances of the symmetric rectangular honeycomb sandwich panels

The nonlinear primary resonances with 1:3:6 of symmetric rectangular honeycomb sandwich panels with simply supported boundaries along all four edges are studied. The nonlinear governing equations of the symmetric rectangular honeycomb sandwich panel subjected to transverse excitations are derived by using Hamilton's principle and Reddy's third-order shear deformation theory. These nonlinear partial differential equations are reduced into nonlinear ordinary differential equations by the Galerkin method. Based on the homotopy analysis method, the average equations of the primary resonance are obtained. For all the three primary resonances cases, the frequency-response curves of primary resonance are constructed. Comparison studies on the forced vibration of cubic non-linearity system are conducted to verify the correctness and accuracy of the homotopy analysis method. Effects of thickness-to-length ratio, width-to-length ratio and transverse excitation on the nonlinear primary response have been investigated for honeycomb sandwich panels.