Vibration Analysis Of An Axially Moving Rayleigh Beam Under Temperature Field

The vibration problem of an axially moving beam under temperature field has attracted more and more researchers’ attention in engineering and engineering fields.As an essential component of engineering field,axial beam has certain theoretical significance and important practical application value in the study of lateral vibration and stability under temperature field.In this paper,the axially moving beam is mainly studied.The main research work is as follows:First,we studied the transverse vibration characteristics of axial beam under temperature field.According to the Kelvin viscoelastic constitutive relation and taking the material time derivative,the generalized Hamiltonian principle is applied to establish the governing equations and related boundary conditions of the coupled plane motion of the beam.Based on the beam theory and the heat conduction equation of the beam considering the influence of deformation,the differential equations of the thermally elastic coupled axially moving beam are derived.Finally,the differential quadrature method is used as the research method,and the influence of temperature on the transverse vibration characteristics of the axially moving beam with thermoelastic coupling was analyzed under different parameters(length-to-height ratio,thermoelastic coupling coefficient,support stiffness and stiffness,etc.).And then,we studied the nonlinear forced vibration of the Rayleigh beam.A dynamic model for nonlinear forced vibration of axial Rayleigh beams is established.According to the Kelvin viscoelastic constitutive relation and taking the material time derivative,the multi-scale method is used to solve the natural frequency and solvability conditions,and the response curves of the first order and the second order under different parameters are given.In the end,differential quadrature was used as the second solution to verify the correctness of the numerical solution.In the end,we studied the combined parameter resonance and main parameter resonance stability of axially variable viscoelastic beams.The Viscoelastic Constitutive RelationsChanged from Kelvin Model to Poynting-Thompson Model.Using the multi-scale asymptotic expansion solution,the solvability conditions are derived.The combined parameter resonance and main parameter resonance stability conditions are given according to the Routh-Hurwitz criterion.Consider the case where the Poynting-Thompson model degenerates into the Kelvin-Voigt model.The numerical examples are used to compare the instability boundaries of the two models.