Experimental and numerical analysis on vibration of plate with multiple cutouts based on primitive cell plate with double cutouts

Abstract

An efficient analytical solution is presented in this paper to model the bending vibration of plates with any numbers of cutouts and under arbitrary boundary conditions. Especially we study the efficiency of the model while explore the influence of increasing number of cutouts and increasing area of cutouts on the eigenpairs of the plate. In the first step, the model of the plate with cutouts is decomposed into certain amount of primitive cells with double cutouts and solved based on the Chebyshev-Lagrangian method. The two advantages of this modeling method lie in offering a flexible assemble strategy of primitive cell plates to form plate in various shapes and with arbitrary numbers of cutouts while bringing substantial convenience in calculation owing to the uniformly expanded double Chebyshev series terms for the displacement of each primitive cell plate. Secondly, the experimental and numerical validations are performed and consequent efficiency and convergence analysis is discussed. The results show that the current model presents potential robust in computation efficiency. At last, the influence of several key parameters on eigenpairs of plate with cutouts is investigated, including the boundary restraint of the plate, the number of cutouts and the size of cutouts.