Nonlinear Vibration Of Axially Moving Eccentrically Supported Beams

Vibration of axially moving beams is an interdisciplinary subject of dynamics,control and solid mechanics.However,the research on axial motion eccentric beam is still very limited.It is of great theoretical significance to study the vibration of an axially moving beam under the condition of eccentricity.The introduction of inhomogeneous boundary condition will have substantial influence on the dynamic behavior of an axially moving beam.Due to the eccentric pulley,the fluctuation of belt tension will cause parameter instability,which will lead to transverse vibration of the structure,which will have an impact on the axial moving beam.The in-depth study of the vibration of an axially moving eccentric braced beam can not only deepen the understanding of the vibration of an axially moving beam,but also enrich the knowledge of the complex dynamics of an infinite dimensional system.Therefore,this research will promote the development of vibration theory of axially moving beams and nonlinear dynamics of infinite dimensional systems.In this paper,the eccentric conveyor belt is taken as the research object.The belt is simplified as an axially moving eccentrically supported beam,and the dynamic models of the axially moving eccentrically supported beam and the axially moving Timoshenko beam are established respectively.The mechanical properties of the axial motion system are studied by the combination of approximate analytical and numerical methods.The specific research contents are as follows:1.Considering the transverse and longitudinal coupling linear vibration model of an axially moving beam under the action of eccentricity,the dynamic stability of the system is obtained by using the direct multi-scale method.The effects of viscoelastic coefficient,axial velocity and stiffness on the stability boundary are respectively considered.At the same time,the influence of internal resonance on the stable boundary was considered.Based on the approximate analytical method and numerical solution,the response amplitude of the midpoint of the beam under the transverse and longitudinal coupling model and the simplified model were compared and verified.2.Considering the transverse and longitudinal coupling nonlinear vibration model of an axially moving beam under eccentric action,the direct multi-scale method was used to obtain the steady-state response of the system.The effects of viscoelastic coefficient,axial velocity,eccentricity and stiffness on the steady-state response were considered respectively.Based on the approximate analytical method and the numerical solution,the response amplitude of the midpoint of the beam under the transverse and longitudinal coupling model and the simplified model were compared and verified.At the same time,the time history diagram,phase diagram and spectrum diagram of the first order primary resonance are given.3.The effects of viscoelastic damping on natural frequencies and attenuation coefficients of axially moving Timoshenko beams are considered.The relationship between axial velocity and related parameters,viscoelasticity and natural frequency and attenuation coefficient were obtained by using the multi-scale method.Finally,the differential quadrature method is used for numerical verification.