Dynamic characteristic analysis of harmonically excited cracked vibration platform with intermediate nonlinear support

This paper investigated the nonlinear dynamics of a cracked vibration platform subjected to a concentrated transverse excitation force considering the structural and supported nonlinearities. To precisely predict vibration properties of the continuum structure, the dynamic model is established based on mechanical relations and the governing differential equations of motion are obtained with the nonlinear regime via an energy method according to the Lagrange's equation, which are discretized by utilizing the Galerkin truncation method. A comparative analysis via the finite element method (FEM) for verification accuracy and convergence is performed. To investigate the influences of the key parameters on the nonlinear behaviors of cracked platform, a wide range of excitation, nonlinear support and crack parameters are analyzed and discussed by bifurcation, time domain for nonlinear mechanics analysis. The numerical results show that a considerable effect of excitation amplitude on the global dynamics for the vibration platform is discovered, namely the higher excitation is able to suppress the chaotic behaviors but increase the vibration amplitude of the system. The increasing nonlinear support stiffness may enhance the chaotic characteristics of the vibration platform, the support position can effectively control the chaotic motion and nonlinear vibration as the support is close to the middle of vibration platform. The crack parameters play an effective role in dynamic behaviors.