Combination reduction dynamic analysis for complex jointed structures with local hysteresis nonlinearity

A combination nonlinear dynamic reduction method is developed to obtain the steady-state dynamic responses of the complex jointed structures having local hysteresis nonlinearity. The harmonic balance method is used to reformulate the nonlinear dynamical governing equations as a set of nonlinear algebraic equations. The local nonlinearity transformation reduction strategy is used to decrease the dimensions of the nonlinear algebraic equations to improve the computational efficiency by defining the local nonlinear contact forces as iteration vector. The transfer functions only related to nonlinear joints are extracted to connect the local nonlinear dynamic responses with the local nonlinear contact forces and external excitations. The Newton’s iteration with the arc-length continuation is then used to obtain the nonlinear solutions. Comparison with the nonlinear dynamic analysis 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 the comparison results of two examples validates the proposed method, and indicates a higher computational efficiency with much less computational costs. Combined with the finite element analysis, the proposed method indicates a potential performance of the nonlinear dynamic analysis of the large-scale complex engineering structures.