Nonlinear oscillations of rectangular plate with 1:3 internal resonance between different modes

The energy transfer between different modes of rectangular plate with 1:3 internal resonance is investigated. The ordinary differential equations of motion for the plate are worked out by applying the Galerkin's method. The nonlinear frequency responses and the waveforms under specific excitation frequencies are obtained by using Runge-Kutta method. The energy transfer process between different modes is analyzed through the waveforms. The results indicate that the energy transfer mode is different when the internal resonance occurs between different modes. In addition, as a result of the presence of in-plane excitation, the internal resonance between two modes can occur when the excitation frequency is not close to any linear natural frequencies.