Response Of A Cracked Non-telescopic Cantilever Beam Excited By Base Noise

A model of a in-extensible cantilever beam with a open surface crack subjected to basal noise excitation is studied.The main purpose of the study is to explore how the cantilever model with a surface crack is affected by the crack and geometric nonlinearity when the cracked cantilever is excited by the Gaussian white noise.A cantilever dynamical model with a open surface crack excited by the pedestal movement with the form of the Gaussian white noise was established in this dissertation.The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained after sufficient consideration of the boundary conditions,the continuous conditions of the crack,and the fracture mechanics.The dynamical equation with the geometrical nonlinearity and the axial inertia nonlinearity which governs the transverse motion was gained with the Kane's method.Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically.The stationary probability density function(PDF)of the amplitude,as well as the joint stationary PDF of the displacement and velocity,was investigated.For the purpose of exploring the reliability of the cantilever,the reliability function was established to avoid the potential fatigue or damage.Numerical simulations were carried out to vindicate the theoretical analysis.The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity.Furthermore,the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation(Monte Carlo method)of the reliability.