Theoretical dynamic reduction for steady-state nonlinear vibration responses of complex jointed structures having hysteretic contact behavior

Abstract

A novel nonlinear dynamic reduction method was developed to determine the steady-state vibration responses of complex jointed structures having hysteretic contact behavior. By using the harmonic balance method to reformulate nonlinear dynamic equilibrium equations into a set of nonlinear algebraic ones, a dynamic reduction technique based on nonlinearity transformation was theoretically developed to iterate nonlinear vibration solutions in the local coordinate that was related only to the degree-of-freedoms of nonlinear joints. Only odd-order harmonic components were truncated to approximate the hysteretic nonlinear contact forces of joint interfaces, which was conducive to further dimension reduction of the nonlinear algebraic equations and iteration matrix. Then, a nonlinear dynamic reduction solver was developed to associate the steady-state nonlinear vibration responses of overall structures with the dynamic characteristics of underlying linear substructures, nonlinear joint models and external excitations. Combined with finite element analysis, the steady-state nonlinear vibration responses of a complex assembled structure with four reduced-order nonlinear joint models were numerically simulated to validate the proposed nonlinear dynamic reduction method by comparing with the literature. The comparative results of nonlinear frequency response functions exhibited good agreement, and the proposed method indicated higher computational efficiency. The experimental investigations of a rubber isolator system were also performed to validate the proposed method, which demonstrated good performance.