Dynamic Response Analysis Of Nonlinear Systems Based On Volterra Series

Engineering structures are nonlinear in nature,However,the nonlinear analysis of structures is very complex,and there is no universal method.In order to obtain an analysis method with strong applicability,Based on the idea of mathematical approximation of structural nonlinear response,Combined with the advantages of Volterra series in describing the nonlinear characteristics of the system,The Volterra series model is used to analyze the nonlinear response characteristics of the structure in this paper.Volterra series is a kind of mathematical functional describing the relationship between excitation and response of nonlinear system,and it is widely used in nonlinear analysis of aeroelasticity,fluid dynamics and mechanical engineering,The main research work includes the following aspects.(1)The properties of Volterra series and the identification method of its kernel function are systematically described,the applicability of different calculation methods in engineering is compared and the principle of least square recursion for Volterra kernel vector is studied.(2)According to the principle of the recursive formula of the least square of Volterra series,the corresponding Matlab program was programmed.The Volterra kernel vector corresponding to the nonlinear response of the system under excitation is solved by the program,the value regularity of kernel function of each order and the accuracy of the kernel vector itself are analyzed.(3)The Volterra series are used in practical engineering,a reinforced concrete frame structure with three floors is taken as the research object,the Volterra kernel function which describes the nonlinear response of the structure under the action of vibration wave is identified by the recursive formula based on the least square method,the accuracy and applicability of kernel function in predicting structural nonlinear response are studied in this paper.