Approximately Analytical Procedure For Stick-slip Vibration System Under Stochastic Excitation

The phenomenon of stick-slip vibration exists in various engineering structures and is often accompanied by random excitation.In order to better control the harm of the stick-slip effect and even make use of this mechanism,it is necessary to study the response of the nonlinear oscillator with stick-slip effect under random excitation,this research has important theoretical significance and good engineering application prospects.In this paper,a single degree of freedom spring-damper-mass-belt system with stick-slip effect under Gaussian white noise excitation is investigated under the assumption that the excitation and damping is low.To analyze this dynamic system,a degenerated system which ignores the viscous damping and random excitation is firstly studied,several typical forms of motion are obtained and it is found that the proportion of the stick phase in the whole motion is small when the belt speed is relatively large.The simplified system which ignores the stick phase therefore can be used instead of the original system under this circumstance.Then the equivalent nonlinear system method and stochastic averaging method are used to study the approximately analytical solution of response of the simplified system under random excitation and it is found that the friction can exhibit conservative and dissipative mechanisms simultaneously.At last,the stochastic averaging of energy envelope is used to investigate the approximately analytical solution of the response of the nonlinear oscillator with stick-slip effect under random excitation,the influence of the system coefficients on response statistics are discussed in detail and it is found that the analytical procedure is valid so long as the portion of stick stage is not too heavyin the stick-slip motion.The belt speed and excitation intensity have significant influences on the random response,and the dramatically different random behavior occurs as these parameters vary.