Research On Multiscale Dynamic Model And Vibration Problems Of Axially Moving Fractional Viscoelastic Beams

In most engineering systems,axially moving viscoelastic beams have important and widespread applications,and the study of their lateral vibration and control problems has important practical application value This article is based on the Euler Bernoulli beam theory and establishes multi-scale dynamic models for three types of axially moving fractional order viscoelastic beams under different displacement and strain relationships,and conducts research and analysis on their vibration problems.Firstly,the force distribution of viscoelastic beam micro elements is analyzed,and the partial differential equation for non linear vibration of the beam is obtained using Newton’s second law and Euler Bernoulli hypothesis In such nonlinear models,the axial stress of the beam is no longer a static value along the entire axis of the beam,but a variable related to the axial coordinates.Therefore,it is necessary to analyze its changes under different conditions Secondly,in the vibration analysis of axially moving beams in this article,the viscoelasticity of the beam material is considered The existence of this viscoelastic damping has a significant impact on the amplitude frequency response of the vibration of the moving beam and the stability of the moving beam under certain excitations.The perturbation method is an effective way to solve the nonlinear vibration problem of axially moving viscoelastic beams with small perturbations;This article mainly uses the improved homotopy perturbation method(HPM)and Adomian decomposition method to solve dynamic differential equations Propose introducing the viscosity coefficient of the beam material into the fractional order and establishing a dynamic model of the viscoelastic beam,analyzing its impact on the vibration of the viscoelastic beam model In this article,the direct multiscale method is used to analyze the vibration problem of axially moving beams,and then the control partial differential equation of the beam is solved based on solvability conditions At the same time,the influence of damping ratio and natural frequency on beam vibration was studied using the established model By comparing three types of models through numerical examples,it was found that fractional order changes have the greatest impact on the displacement strain relationship based fractional order viscoelastic beam model,damping ratio changes have the smallest impact on the Lagrange strain based fractional order viscoelastic beam model,and fixed frequency changes have the greatest impact on the shear strain based fractional order viscoelastic beam model.