The Dynamics Of Axially Moving Viscoelastic Plates With Time-variant Tension

In the fields of nature,practical life,and engineering practice,many motion structures can be reduced to axial motion structures.Such models include elevator elevator cables,band saws,textile fibers and conveyor belts.When there are parametric excitations,they will generate large lateral vibrations.The introduction of axial velocity and tension(instantaneous change in tension)will have a significant effect on the dynamic characteristics of the axial motion structure.They will also lay the foundation for future research on more complex physical models.The research object of this paper is axially moving viscoelastic plate.Firstly,the dynamic model of axial viscoelastic plate is established by using energy method and Kelvin's viscoelastic constitutive relation.Then the approximate analytical method and numerical method(differential quadrature method)are used,Comparative verification analysis of the dynamic behavior of axially viscoelastic plates.The specific research content is as follows:Firstly,establish the dynamic model of the axially moving viscoelastic plate under time-varying tension.Firstly,we use the generalized Hamilton principle to introduce the cyclically varying tension and derive the corresponding pulsation velocity.Then,considering the viscoelastic constitutive relation of the Kelvin model,the vibration of the axially moving viscoelastic plate under time-varying tension is derived.The control equations and their corresponding non-homogeneous boundary conditions.It also lays the foundation for the theoretical model for the following research.Secondly,introduce the factors of the axial tension change with time in the system,and analyze the instability of the linear parametric vibration of the axially moving viscoelastic plate.Firstly,based on the established model,the equations of axially moving viscoelastic plates and the corresponding non-homogeneous boundary conditions under the action of time-varying tension are deduced.Then,the direct multiscale method is used to approximate the analytical solution of the system and itsmodal function and natural frequency.Finally,the initial conditions of the system are brought into the control equation,and the final analytical results are verified by the differential quadrature method.The parameter coefficients have an effect on the instability of the system when there is a 1:3 internal resonance.Thirdly,introduce the factors that change the axial tension with time in the system,and analyze the nonlinear parametrically excited vibration of the axially moving viscoelastic plate.Similar to the linear parametric vibration,first,based on the established model,the relationship between the time-varying tension and the axial velocity and its corresponding nonlinear term are introduced,and the axial motion viscoelastic plate is deduced in this case.The control equations and its non-homogeneous boundary conditions.Then using the direct multi-scale method and Routh-Hurwitz criterion to solve the system's instability response.Finally,the initial conditions of the system modeling are brought into the control equation,and the differential analysis method is used to verify the final analysis.