Finite element computation of nonlinear modes and frequency response of geometrically exact beam structures

Abstract

An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the cross-section can be extreme. The FE equation is solved by a combination of harmonic balance (HBM) and asymptotic numerical (ANM) methods. The novel solving scheme is rooted entirely in the frequency domain and is capable of computing both the structure’s frequency response under periodic external forces as well as its nonlinear modes. An overview of the proposed numerical strategy is outlined and simulations are shown and discussed in detail for several test cases.