Modelling and vibration analysis for the multi-plate structure connected by nonlinear hinges

Abstract

The dynamic modelling approach for the multi-plate structure connected by nonlinear hinges is presented in this paper. The Chebyshev polynomials are employed as admissible basis functions to establish the dynamic model of each plate. The Lagrange multiplier is introduced to describe the restraint effect of the hinge on the plate. In order to show the impact of the hinge on the plate as reasonably as possible, the constraint contains not only the displacement of each plate but also the rotation of adjacent plates. Then based on the Rayleigh-Ritz method, a characteristic equation is derived and natural frequencies of the multi-plate structure are obtained. Considering the cubic nonlinearity and Coulomb friction of the hinge, the discrete dynamic model of the multi-plate structure is established according to the obtained modal shape functions. Comparing the natural frequencies and modal shapes of the analytical model with that of the finite element model, the validity of the present method and the accuracy of the model are demonstrated. Simulation results show that linear modes play an important role in the dynamic analysis. By varying the relevant parameters (structural and excitation's) and conducting a nonlinear response, their effect on the dynamic response of the whole structure is demonstrated.