Stochastic Vibration Responses Of Controllable Nonlinear Viscoelastic Composite Structures

In this paper,the random vibration response of the composite structures with the nonlinear adjustable viscoelastic is studied.The controllable nonlinear viscoelastic sandwich beam,the controllable nonlinear viscoelastic sandwich vertical beam and the viscoelastic periodic pole are used as the model.The nonlinear random vibration responses of the controllable nonlinear viscoelastic sandwich beam and sandwich vertical beam under random excitation,and the transient and steady state and random vibration responses of the longitudinal vibration of the viscoelastic periodic pole under periodic excitation are studied by using the theory and numerical simulation method.This study have enriched the research results of nonlinear random vibration of composite structures.The main work of this paper is as follows:1?The nonlinear random vibration responses of the controllable nonlinear viscoelastic sandwich beam and its supporting mass system under random excitation is studied.In this paper,a nonlinear dynamic model is used for describing the viscoelastic constitutive relation.The differential equations of motion of a viscoelastic sandwich beam under stationary random support excitations are derived and converted into nonlinear multi-mode coupling vibration equations by using the Galerkin method.The equivalent quasi-linear system is derived by using the statistic linearization method.The random responses of the nonlinear random vibration are obtained.The effects of the physical and geometric parameters of the viscoelastic body and the size of the sandwich beams and the excitation spectrum on the root-mean-square(RMS)displacement are investigated by a large number of numerical computations by Matlab,which are studied under the two conditions of hard nonlinearity and soft nonlinearity for the viscoelastic body.The results show that the physical nonlinearity of the controllable viscoelastic body has a significant influence on the nonlinear response of sandwich beam whether it is hard nonlinear or soft nonlinear.And the controllable viscoelastic body can effectively suppress the nonlinear random vibration response of the sandwich beam.2?The nonlinear random vibration responses of the controllable nonlinear viscoelastic sandwich vertical beam under random excitation is studied.In this paper,a nonlinear dynamic model is used for describing the viscoelastic constitutive relation.The differential equations of motion of a viscoelastic sandwich vertical beam under stationary random support excitations are derived and converted into nonlinear multi-mode coupling vibration equations by using the Galerkin method.The equivalent quasi-linear system is derived by using the statistic linearization method.The random responses of the nonlinear random vibration are obtained.The effects of the physical and geometric parameters of the viscoelastic body and the size of the sandwich vertical beam and the excitation spectrum on the root-mean-square(RMS)displacement are investigated by a large number of numerical computations by Matlab,which are studied under the two conditions of hard nonlinearity and soft nonlinearity for the viscoelastic body.The results show that the physical nonlinearity of the controllable viscoelastic body has a significant influence on the nonlinear response of sandwich vertical beam whether it is hard nonlinear or soft nonlinear.And the controllable viscoelastic body can effectively suppress the nonlinear random vibration response of the sandwich vertical beam.It can be seen that the similar theoretical methods are used to study the random responses of the controllable nonlinear viscoelastic sandwich beams and sandwich vertical beams.But in the process there are big differences.For example:The modal functions of the vertical beams are essentially different with the beams,and the boundary conditions of the vertical beams are more complicated,and the researchs are much more difficult than the beams.3.The transient and steady state vibration responses of the longitudinal vibration of the viscoelastic periodic pole under periodic excitation and the random responses of longitudinal vibration of the viscoelastic periodic pole under random excitation are studied.Firstly,based on the theory of random vibration,the longitudinal vibration equation of the periodic beam is established.Secondly,the vibration equation is transformed into ordinary differential equations by Galerkin method,so,the multi-degree-of-freedom vibration equation of the periodic beam is obtained.Finally,the influences of geometric and physical parameters,excitation frequency,position of excitation points and response points on the root-mean-square(RMS)displacement of the transient and steady state vibration responses of the periodic pole are investigated by a large number of numerical computations by Matlab.It is found that the effects of the parameters of viscoelastic supports are significant on the transient and steady state vibration responses and random responses of the longitudinal vibration of the viscoelastic periodic pole.In conclusion,the random vibration responses of the controllable nonlinear viscoelastic composite structures are studied by means of theoretical and numerical simulation methods,and the corresponding calculation methods are developed.The research results of this paper provide a new theoretical basis for the design of nonlinear viscoelastic composite structure and its application in the fields of structural damage detection technology,aerospace and precision machine vibration control.