Modal analysis for random vibration of hysteretic frames

Abstract

AbstractAn algorithm is presented for the direct stiffness formulation of hysteretic frames which is suitable for random vibration analysis under zero mean or non‐zero mean random excitation. A modal transformation is used to reduce the number of active degrees of freedom. First and second order response statistics are presented for two example frames using stochastic equivalent linearization and Monte Carlo simulation. The modal transformation stabilizes the stationary response calculation algorithm by eliminating superfluous higher modes. The iterations for transient response calculations under non‐zero mean excitations are destabilized by elimination of too many modes. The modal transformation allows reasonable response estimates to be obtained with significant reductions in computing time. The expected lower modes dominate the response, but inclusion of several higher modes is necessary to provide reasonable response estimates.