Equivalent linearization method improved by higher order statistics in modal space for geometrically nonlinear vibrations

Abstract

In this paper, an equivalent linearization method considering higher order statistics based on nonlinear reduced order modeling techniques is proposed for the geometrically nonlinear random vibration problems of complex structures. Nonlinear reduced order models of the structures are constructed by leveraging the nonlinear analysis capabilities of commercial finite element codes, and an improvement to the Stiffness Evaluation Procedure method for determining the stiffness coefficients is achieved through the equivalence relation, leading to a notable reduction in computational cost with no further requirements for commercial finite element codes. The nonlinear terms are twice regulated equivalent, and then a regulated form of the stiffness coefficients is derived to introduce higher order statistics into the equations of motion. Then a linearized system obtained by the criterion of force error minimization is used to predict the random response of the original nonlinear system. The nonlinear problems are solved by the linearized system in the modal space, increasing computational efficiency significantly. Higher order statistical information of the response is introduced to improve the accuracy. Typical examples are used to verify the effectiveness of the proposed method, while its applicability is further demonstrated via the analysis of turbulence-excited composite laminates.