Vibrational analysis of finite plate on elastic foundation subjected to oblique impact

Abstract

As a typical nonsmooth strong coupling dynamic problem, the vibrational analysis on the plate subjected to the oblique impact requires us to develop the effective method that can be used to deal with the nonsmooth strong coupling problem well. Focusing on the local dynamic behaviors of the impact system, the generalized multisymplectic method is employed to reproduce the dynamic response of the finite plate on the elastic foundation subjected to an oblique impact in this paper. Firstly, the first-order approximate symmetric form of the dynamic equation describing the vibration of the finite plate on the elastic foundation subjected to an oblique impact is deduced based on the multisymplectic theory. Then, a generalized multisymplectic scheme equivalent to the Preissmann scheme for the first-order approximate symmetric form is constructed. The validity as well as the high precision of the generalized multisymplectic scheme are verified by the finite element method and the approximate theoretical solution in the numerical simulations finally. From the numerical results, the effects of the angle parameters for the oblique impact on the maximum transverse displacement of the plate are discussed in detail. The main contribution of this work is proposing a structure-preserving method to investigate the nonsmooth strong coupling dynamic problem effectively.