Large displacement behavior of a rocking flexible structure under harmonic excitation

Abstract

In this paper the nonlinear dynamic behavior of a rocking flexible structure subjected to harmonic excitation is investigated. The dynamic response of the structure is characterized by a sequence of full contact and rocking phases which may be halted by the overturning of the system. In the study, reference is made to a simple lumped mass model which, in the full contact phase, behaves as a linear single degree-of-freedom system. In the rocking phase the system exhibits two degrees of freedom and its response is evaluated with reference to large rigid rotations and small elastic deformations. New explicit and numerical results are presented as a function of structural and loading parameters. The complex dynamic behavior of the rocking flexible structure, subjected to harmonic excitation, is compared with the corresponding nonlinear dynamics of the rigid system with the aim of highlighting the limits of applicability of the rigid body assumption. Extensive numerical applications have been performed in order to evaluate the main features of the nonlinear response of the flexible model subjected to harmonic acceleration at the base.