Multiple Periodic Vibrations of Auxetic Honeycomb Sandwich Plate with 1:2 Internal Resonance

In this paper, we focus on the multiple periodic vibration behaviors of an auxetic honeycomb sandwich plate subjected to in-plane and transverse excitations. Nonlinear equation of motion for the plate is derived based on the third-order shear deformation theory and von Kármán type nonlinear geometric assumptions. The Melnikov method is extended to detect the bifurcation and multiple periodic vibrations of the plate under 1:2 internal resonance. The effects of transverse excitation on nonlinear vibration behaviors are discussed in detail. Evolution laws and waveforms of multiple periodic vibrations are obtained to analyze the energy transfer process between the first two order modes. Even quite small transverse excitation can cause periodic vibration in the system, and there can be at most three periodic orbits in certain bifurcation regions. The periodic orbits are classified into two families by tracing their sources. The study provides the possibility for the classification study on generation mechanism of system complexity and energy transfers between different modes.