Nonlinear Vibration Analysis Of An Axially Moving Beam Under Random Excitation

Since the beam system has a wide range of applications in various fields,and there are often various nonlinear factors in the beam system,it is very important to carry out the research work of the beam system.In this paper,the dynamic response of axially moving beams under random excitation is studied.Firstly,the dynamics of the beam is modeled by the micro-element method.Then the total energy equation of the axially moving beam system is established by Hamilton principle and expressed in a dimensionless form.Then the stochastic averaging method is used to derive the corresponding average stochastic differential equation.On this basis,the corresponding FPK equations and backward Kolmogrov equations are established and solved respectively.The dynamic characteristics of system response and reliability are studied.The effectiveness of the proposed method is verified by numerical simulation.The second chapter mainly introduces the Hamilton principle and several research methods of axial moving beam,and briefly describes the numerical solution of differential equations.The third chapter mainly expounds the stochastic average method and introduces the stochastic averaging of amplitude envelope suitable for weakly nonlinear systems,the strongly nonlinear stochastic averaging method for strong nonlinearity and the stochastic averaging of energy envelope.Finally,a quadratic nonlinear vibration system under random excitation is used as an example to verify The validity of the proposed stochastic averaging method;In the fourth chapter,the dynamic model of the axial moving beam system is established based on the micro-element method and Hamilton principle.Then the equation is discretized by Galerkin method and finally expressed as a dimensionless differential equation with parameter random excitation.The dynamic characteristics of the axial moving beam system were studied by stochastic average method.This chapter analyzes the energy characteristics of the axial moving beam,the steady-state probability density of the system response,the reliability and first-passage time of the system.The steady-state probability density of the system amplitude and the steady-state probability density of the total energy of the system under different noise intensities and different system parameters are studied.The effects of system parameters on the reliability and the first-passage time are investigated.Finally,all the theoretical results are verified by Monte-Carlo simulation.