Vibration Analysis And Simulation Of Axially Moving Viscoelastic Beams Based On Galerkin Method

The model of axially moving beam and axially moving sandwich beam is widely used in engineering.The model has the advantages of wide application range,strong equivalence and large controllability.Galerkin method is an approximate numerical method based on the principle of weighted residual,which has high accuracy and strong operability.By using high-order Galerkin truncation,the nonlinear partial differential vibration equation of moving beam system can be precisely discretized into ordinary differential equation,which lays a good foundation for later vibration analysis and finite element validation analysis.Based on the research of beam structure by predecessors at home and abroad,the eighth-order truncation of an axially variable speed viscoelastic moving beam system is carried out by Galerkin method,and the nonlinear parametric vibration and stability of axially moving viscoelastic beam are studied by discretizing into ordinary differential equations.Aiming at the axially viscoelastic composite sandwich beam,the linear and non-linear vibration of axially moving composite sandwich beam is studied.The vibration equation of the system is established by using Kelvin viscoelastic classical model.The vibration equation is discretized by Galerkin method,and then the vibration shadow of the sandwich beam is orderly affected by natural frequency,boundary conditions,inherent parameters of the system,external excitation and axial velocity.The noise was studied in detail.Then,based on the finite element method and ANSYS simulation software,the sandwich beam is further simulated and the results and rules of the previous research are verified.At the same time,considering the special conditions,sandwich beams work under variable temperature conditions,there is a problem of temperature stress.The thermodynamic analysis of sandwich beams is carried out by using finite element method,which provides more comprehensive data support for practical engineering applications.Through the comprehensive application of Galerkin method and finite element method,the calculation of axially moving beam and sandwich beam system is validated and compared with the authoritative literature.The accuracy of the numerical results and the scientific nature of the research method are proved.The vibration law,the distribution of the stability region and the thermodynamic law of the axially moving viscoelastic beam system are obtained.