A nonlinear dynamic reduction solver for complex jointed structures having hysteresis contact behaviour

Abstract

Abstract A novel nonlinear dynamic reduction method was developed to determine the steady-state vibration responses of complex jointed structures having hysteresis contact behaviour. By using harmonic balance method to reformulate the nonlinear dynamic equilibrium equations into a set of nonlinear algebraic ones, a dynamic reduction strategy of local nonlinearity transformation was theoretically developed to iterate nonlinear solutions in the coordinate associated with the degree of freedoms of the nonlinear joints. Only odd-order harmonic components were truncated to approximate the hysteresis nonlinear contact forces of the joint interfaces, as this approach was conducive to the further dimension reduction of nonlinear algebraic equations and iteration matrix. Then, a nonlinear dynamic reduction solver was developed to bridge the steady-state nonlinear vibration responses of the overall structure with the dynamic characteristics of the underlying linear substructures, nonlinear joint models and external excitations. Combined with the 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. The comparative results shown a good agreement with the literature work, and indicated a great higher computational efficiency. The experimental investigations of a rubber isolator system were also performed to validate the proposed method, and presented a good performance.