Intermediate Constrained Control And Nonlinear Absorption For Nonlinear Vibration Of Axially Moving Continuum

Elastomers driven or flowing along the axis are common basic components in engineering systems,such as conveyor belts,aerial cable cars,high-rise elevator cables and pipelines for conveying fluid.Axial velocity causes large lateral vibration of the axially moving continuum,which affects the service performance and service life of the equipment,and seriously restricts the development of the equipment to high-end.Aiming at the requirement of harmful vibration suppression of axially moving continuum in engineering,the vibration characteristics and vibration control of axially moving continuum with intermediate elastic constraints are studied.The dynamic model of axially moving continuum with intermediate elastic constraints is established.The effects of intermediate elastic constraints on natural frequencies and stimulated vibration responses of the system are studied by approximate analytical and numerical methods,and the intermediate nonlinearity is also studied.The specific contents are as follows:(1)Based on the generalized Hamilton principle,the dynamic model of an axially moving beam with intermediate spring constraints is established.The transverse free vibration characteristics and nonlinear forced vibration response of axially moving beam with trapezoidal cross section are studied by Galerkin method.The influence of intermediate restraint spring on the natural frequencies of transverse free vibration and the steady-state response of nonlinear forced vibration of axially moving continuum is emphatically discussed;(2)The transverse vibration characteristics of axially moving beams with intermediate elastic constraints are studied for the first time by using a two-span beam model,in which the constraints are regarded as boundaries.The approximate analytical solution of the natural frequency of transverse vibration of an axially moving beam is obtained by the complex mode method.By comparing the results with those of Galerkin method,the correctness of the analysis results of axially moving continuum with intermediate constraints in previous single-span beam model studies is proved;(3)The suppression of transverse vibration of pipeline by intermediate nonlinear energy sink(NES)is studied.The dynamic model of the nonlinear coupling between the transverse vibration of the pipeline and the NES vibration absorber is established.Combining the complexification-averaging method with the arc-length continuation method,the transverse nonlinear forced vibration response of a pipeline with a non-linear energy absorber in the middle is studied,and the approximate analytical analysis of the steady-state response is verified by numerical method.The results show that the nonlinear energy sink can effectively suppress the transverse vibration of the pipeline.In summary,through this study,a two-span beam model is established to study the transverse vibration characteristics of axially moving beams constrained by intermediate springs,which proves the validity of previous single-span beam model research results.The approximate analytical and numerical methods for transverse nonlinear vibration of pipelines with a nonlinear energy sink are developed,the vibration suppression mechanism of the nonlinear energy sink of the axially moving continuum is clarified,it provides a new idea and theoretical basis for nonlinear vibration control of axially moving continuum.