A new approach to model a system with both friction and geometric nonlinearity

Abstract

This paper presents a new reduced-order model that can capture the nonlinear dynamics of a structure containing both friction and geometric nonlinearity, and proposes a procedure to derive the parameters of the model from quasi-static simulations. The Single-mode Implicit Condensation and Expansion (SICE) method was recently shown to be capable of capturing the resonant behavior of a geometrically nonlinear structure, and the modal Iwan model has proven effective at capturing the hysteretic behavior of a mode that exhibits nonlinearity due to friction. This paper combines the two into a new model, referred to here as the Iwan model with Geometric Nonlinearity (or the IGNL model). It consists of an Iwan model with an additional spring-slider unit, where the slider has infinite strength and the spring consists of polynomial terms that define the SICE-ROM. A procedure is also proposed to use Quasi-Static Modal Analysis (QSMA) to estimate the parameters of the IGNL model from a set of nonlinear force–displacement curves. Existing literature shows how QSMA can be used to characterize the force–displacement behavior of a nonlinear mode where the nonlinearity is due to friction or bending–stretching coupling, but not both simultaneously. This paper proposes certain adjustments to the QSMA procedure so that the two forms of nonlinearity can be isolated. Two case studies are presented to test the efficacy of the IGNL model, one consisting of a simple spring–mass model and the second, a finite element model containing both contact and geometric nonlinearity. The proposed method is shown to be significantly faster than performing dynamic simulations to estimate the amplitude-dependent frequency and damping behavior.