Incremental Hamilton's principle with multiple time scales for nonlinear aperiodic vibrations of shells

Abstract

It has been previously provided an extension of the Incremental Harmonic Balance (IHB) Method to aperiodic vibrations of nonlinear systems by introducing the concept of multiple time scales (dimensions), where the solution is assumed to be a combination of sinusoidal terms of incommensurable frequencies. This extended numerical technique is of practical significance as in many cases only the aperiodic vibrations exist in a nonlinear system. To illustrate the wide applicability of the method and also for later use, this paper will present an incremental Hamilton's principle with multiple time scales for thin plates and shallow shells. Refs.