Asymptotic estimation of free vibrations of nonlinear plates with complicated boundary conditions

Abstract

We consider the modified method of parameter continuation (MMPC) as an asymptotic technique for estimating the frequencies and shapes of nonlinear oscillations of plates with complicated boundary conditions. Unlike the Bolotin’s method, which is usually used for such estimations, MMPC estimations depend from the shape of initial perturbation. When the perturbation coincides with the eigenform of plate vibration, then its frequency close to the relevant eigenfrequency. In another cases, however, it describes real vibration shape of plate with different conditions on its edges. The comparison with numerical calculations confirms the advantages of proposed method and its accuracy.