Stochastic equivalent linearization (SEL) method has gained wide popularity because of its versatility in application to multiple-degree-of-freedom (MDOF) nonlinear systems. It is restricted in the random vibration analysis of flexible structures because of the implicit nonlinear system. This paper presents a new method for the equivalent nonlinear system of flexible structures. Using this method, the implicit geometrically nonlinear system can be represented as an explicit equivalent nonlinear system. According to the modal analysis method, the geometrically nonlinear force is replaced by a high-order moment of modal coordinate. The MDOF physical system is translated into a modal system, which could be solved easily. Based on the equivalent nonlinear system, the nonlinear random vibration method is presented by using SEL technology. By using the pseudo-excitation method, the efficiency of the nonlinear random vibration method is increased obviously. The rapid calculation makes it possible to analyze the nonlinear random vibration of MDOF flexible structure. The validation shows that the method has reasonable precision and high efficiency and it could be used in the random vibration analysis of practical flexible structures.
Equivalent linearization method using Gaussian mixture (GM-ELM) for nonlinear random vibration analysis