Random vibration and global dynamic analyses of nonlinear MDOF systems under combined additive and multiplicative excitation

Abstract

The random vibration and global dynamic analyses of structures subjected to combined additive and multiplicative excitation are challenging issues. In this paper, the direct probability integral method (DPIM), as a novel method, is developed to address these issues. The first aim of the paper is to investigate the random vibration responses of multi-degree-of-freedom (MDOF) systems under combined excitation by DPIM, showing the evolutionary process of probability density functions of the response. The second aim is to illustrate the global dynamics of MDOF systems under combined excitation. By incorporating the ?-committor functions, a DPIM-based strategy is proposed to obtain the generalized stochastic basins of attractions of system and evaluate the corresponding stochastic basin stability through global integrity measure (GIM). In the numerical example, the stochastic dynamic analysis of nonlinear MDOF coupled ship model under random oblique wave is performed, demonstrating the accuracy and efficiency of DPIM by comparing with Monte Carlo simulation (MCS) method. It is also indicated that the safety basin of ship can be effectively represented in a probabilistic way, and the erosion of stochastic safety basin will be appeared with increase of significant wave height.