Approximating nonlinear response to harmonic base-excitation using fixed-interface quasi-static modal analysis

The recently developed quasi-static modal analysis (QSMA) technique approximates the amplitude dependent modal characteristics of large-scale finite element models with frictional contact at preloaded interfaces. The nonlinear natural frequencies and damping ratios offer insight into the dynamic behavior of assembled structures, particularly the amount of frictional damping and stiffness loss introduced from an isolated modal oscillation due to the joints. This work presents an approach to approximate the nonlinear steady-state response of a base-excited structure using the nonlinear frequency and damping estimates from QSMA. A Hurty/Craig-Bampton transformation allows for the base-excited system to be expressed in terms of the fixed-interface modal coordinates, thus allowing the extension of previously developed analytical approximations using the prescribed base acceleration and the nonlinear, fixed-interface modes from QSMA. The accuracy and relevance of this non-intrusive approach rely on the applicability of Masing's hypothesis within QSMA to approximate the hysteresis curves from the initial loading curve. The limitations are investigated by considering both Masing and non-Masing joint models. A comparison to reference solutions demonstrates the accuracy of the approximation to efficiently obtain nonlinear steady-state solutions of large-scale models with frictional interfaces for cases that satisfy Masing's hypothesis.