Modeling And Dynamic Characteristic Analysis For Nonlinear Systems With Freeplay Based On Mode Synthesis Method

With the development of high-speed and large-capacity electronic computers and finite element analysis software,finite element modeling has gradually become an effective numerical analysis method for solving structural dynamic problems,and has been widely used in engineering fields including aerospace,mechanical,civil and shipbuilding engineering.However,for complex structural systems using a large number of nonlinear connecting elements,it is difficult to accurately and efficiently model and analyze the system based on the finite element method.Freeplay in the interface is one of the important reasons for the nonlinear behavior of the structure.Freeplay nonlinearity changes the stiffness characteristics of the structure,which has an important impact on the dynamic characteristics of the structure.This paper solves the problem of nonlinear system modeling and dynamic characteristics analysis by finite element modeling,modal synthesis methods and model updating in an effort to provide theoretical basis and technical support for dynamic analysis of the freeplay nonlinear system in engineering practices.The main content of the paper are as follows:(1)The first chapter introduces the research background and significance of nonlinear systems with freeplay,and the research status of modal synthesis methods and the model updating methods of structural dynamics.The necessity of modeling and dynamic analysis of nonlinear systems with freeplay based on modal synthesis method is subsequently presented.(2)The second chapter elaborates the model reduction theory based on the free interface mode synthesis method,and also introduces the residual mode solution method for the substructure with or without rigid body modes.Different connection interfaces(rigid connection interface,elastic connection interface,and rigid-elastic connection interface)are respectively introduced,and overall dynamic equation of the systems considering external excitation or nonlinear connection boundary are respectively discussed.(3)The third chapter establishes the finite element model of the cantilever plate,and reduces the finite element model of the cantilever plate to obtain its substructure model through the free interface modal synthesis method.The accuracy of the substructure model is tested by the comparison of natural frequencies and responses in a linear case between the finite element model and substructure model.The substructure model of nonlinear cantilever plate with freeplay is further established,and the nonlinear dynamic characteristics of the structures are analyzed based on responses and sweep curves.Thus the feasibility of the free-interface modal synthesis method for nonlinear system modeling with freeplay is verified.(4)The fourth chapter establishes the finite element model of the overhanging beam,and then it is reduced by the modal synthesis method.Next,the freeplay nonlinear connection stiffness at the joint boundary is obtained by model updating,and the nonlinear dynamic model of the overhanging beam with freeplay is established.As a result,the nonlinear dynamics of the overhanging beam are analyzed based on the nonlinear dynamics model.(5)The fifth chapter builds the finite element model of a folding fin,and the model of the folding fin is reduced by the free interface modal synthesis method.The nonlinear connection stiffness of the freeplay at the connection boundary is obtained by model updating,and then the nonlinear dynamic model of the folding fin with freeplay is established.The nonlinear dynamics of the folding fin is thus analyzed based on the nonlinear dynamic model.