Frequency domain method for random vibration analysis of nonlinear systems under time-varying coherent nonstationary excitations

Strong earthquakes, downbursts, and typhoons are extreme events that involve time-varying coherent excitations, which are crucial in accurately analyzing the structural response. However, most current methods for nonstationary random vibration analysis assume time-invariant coherence, which fails to capture the time-varying nature of real-world excitations. To address this gap, this study proposes an effective and efficient frequency domain analysis framework for nonlinear systems under time-varying coherent nonstationary excitations. This framework is grounded in the equivalent linearization technique and an enhanced evolutionary spectral method (EESM). Through the use of the equivalent linearization technique, a series of equivalent linear systems replaces the initial nonlinear system; with EESM, the highly efficient analysis of time-varying coherent nonstationary random vibrations in linear systems can be performed, requiring only a limited number of time history analyses and fast Fourier transform operations. For local nonlinear systems, the efficient frequency domain method is more favorable in terms of efficiency due to the explicit calculation advantages of EESM. The specific applications for Duffing system and hysteretic system are presented to demonstrate the reliable accuracy and exceptional efficiency of this method, thereby showcasing its potential in addressing large-scale nonlinear system problems.