Investigating nonlinear modal energy transfer in a random load environment

Abstract

When a structure is subjected to an extreme environment, its linear normal modes, which are uncoupled under small loads, begin to influence each other and exchange energy. This is easily explained when the nonlinear normal modes of the structure are computed, since they show internal resonances where the underlying linear modes combine to produce the NNM solution at each excitation level. This paper examines the degree to which nonlinear modal coupling can serve as an energy transfer mechanism in order to reduce the vibration levels of a structure subjected to a broadband, random forcing. The structure in question is a beam with an intermediate support that is adjusted in order to vary the frequency ratios between modes. To explore the significance of modal coupling, two types of reduced order models are examined: A customary model including all of the coupling terms between the linear modes, and an uncoupled reduced order model which contains nonlinear stiffness terms in single modes only. The differences in response between the two models are used to quantify the effect of nonlinear modal coupling in the structure.