An improved nonlinear dynamic reduction method for complex jointed structures with local hysteresis model

Abstract

An improved nonlinear dynamic reduction with the harmonic balance method is developed to approximate the steady-state vibration responses of the complex jointed structures having local hysteresis nonlinearity. The modal superposition method combined with the static stiffness compensation is used to degrade the mode truncation effects on the transfer functions by using only one concerned dominant mode. The local nonlinearity transformation reduction is used to decrease the dimensions of nonlinear algebraic equations and iteration matrix by defining the local nonlinear contact forces as the iteration vector. The transfer functions only related to the nonlinear joints are extracted to connect the local nonlinear dynamic responses with the local nonlinear contact forces and external excitations. The local nonlinear contact forces are consequently updated. The discrepancy between the given local nonlinear contact forces and updated ones is used to construct the residual error functions to update the iteration vector to obtain the nonlinear solutions. Comparison with the generalized modal superposition and full order methods in the literature is performed to validate the proposed method by using a lap-type bolted joint beam system and a complex jointed structure. The good agreement of comparison results of two examples validates the proposed method, and indicates a higher computational efficiency. The effective construction of the transfer functions plays a critical role in predicting the steady-state nonlinear dynamic responses of the complex jointed structures, and consumes a lot of computational costs.