Influence of geometric nonlinearity of rectangular plate on vibration reduction performance of nonlinear energy sink

The differences between the vibration reduction of a NES (nonlinear energy sink) on a nonlinear plate and a linear plate are compared, and the effect of NES on the nonlinear plate is mainly analyzed. The nonlinear equations of the plates connected to NES are derived and subsequently solved by the complexification-averaging method and least square method. The amplitude of the first mode of the nonlinear plate is several times higher than that of the linear plate under large excitation when the two plates are attached to identical NES. The amplitudes of the second mode of the two NES equipped plate are similar. However, super-harmonic resonance responses of the two systems are significantly different. The evolution of the higher branch responses in super-harmonic resonance frequency band of the second mode is analyzed, and found to be significantly different with respect to that in the primary resonance frequency band of the first mode.