Dynamics of a rectangular thin plate with lumped mass under harmonic foundation and in‐plane excitations

Abstract

Nonlinear dynamic behaviors including global bifurcations and multi‐pulse chaotic dynamics of a rectangular thin plate with lumped mass subjected to a harmonic foundation excitation and in‐plane excitation are investigated in this paper. With the von Ktrueármtrueán equation and Galerkin method, the dynamic equation of the first two modes for this model is obtained. Utilized the method of multiple scales, the average equation of the system in the case of both primary resonance and 1/2 subharmonic resonance is obtained. Global bifurcations and chaotic dynamics of the rectangular thin plate are analyzed with the energy‐phase method. The effect of the dissipation factor on pulse sequence and layer radius is discussed in detail. The results obtained here indicate that there exist Silnikov‐type multi‐pulse orbits homoclinic to certain invariant sets for the resonant case, which means that chaotic motion may occur. Homoclinic trees describing the repeated bifurcations of multi‐pulse solutions are also obtained. With the Runge–Kutta method, numerical simulations including the time histories and phase portraits are given, which demonstrate that chaotic behaviors may occur and confirm the analytical results.