The Research On Non-random Vibration Analysis Of Elastic Beams Subjected To Uncertain Moving Loads And Its Application

The model of vibration of elastic beam under the excitation of moving loads is a kind of important model in daily life and engineering problems.The most typical problems in engineering may be the problem of automobiles and trains crossing bridges.With more rigorous requirements on analysis results of this kind of problem,the deterministic model is no longer able to describe the actual working mechanism and predict the response of the structure accurately.For example,in the problem of vehicle crossing bridges,the force acting on the bridge is not constant.In view of the uncertainty,most scholars resorted to random process to model and describe the uncertain dynamic load and developed the corresponding method to deal with this sort of problem,namely random vibration analysis method.However,the premise of application of the random process model is to obtain the dynamic probability distribution information of uncertain dynamic loads.Unfortunately,it is not easy to construct the premise in all cases.In the meanwhile,the structural uncertainty analysis based on interval process stands out for its simplified procedure of modeling,less sample capacity and practical application in engineering.Therefore,the interval process model is applied to describe the uncertain load moving across the beam.Based on the classical elastic beam vibration theory and the interval process model,the upper and lower boundary of the vibration response of the elastic beam under the excitation of uncertain moving load(s)is derived.Consequently,the nonrandom vibration analysis method of elastic beam based on interval process model is established.The paper intends to do something to explore for the more application of interval process model in uncertainty problems.The work of this paper includes the following contents:(1)The mechanical model of elastic beam vibration due to the excitation of moving load(flow)excitation is derived from a type of typical engineering problems.The vibration theory of elastic beam is introduced.The classical analytic solution and more systematic analysis are given for the vibration of elastic beams excited by a single deterministic moving load and a stream of deterministic moving loads.(2)An interval process model is introduced to describe the uncertainty of uncertainty of the moving load.The dynamic parameters in the interval process model are characterized as two dynamic boundary curves and are interval at each instant.The establishment of interval process model requires only the dynamic boundary information and the correlation information between different instants.(3)The interval process model is applied to describe the uncertainty of the moving load.Based on the properties of the interval process and the vibration theory of the elastic beam,the analytic expression of the dynamic response boundary of the elastic beam is derived.By means of the non-random vibration analysis method proposed,two typical engineering problems,the vibration of bridge and slender workpiece are analyzed systematically.The boundaries of deflection response of the bridge and slender workpiece is obtained,and the influence of various parameters on deflection response of the bridge and workpiece is analyzed.(4)In view of the actual service condition of trains and vehicle streams passing through a bridge,the vibration problem of elastic beam excited by uncertain moving load streams are studied.The models of trains and vehicle streams moving across a bridge are researched respectively,in which the resonance and cancellation effects are studied.The interval process model is introduced to describe the uncertain moving load streams,and the boundaries of dynamic response of the elastic beam subjected to the uncertain moving load streams are derived.The work condition and parameters of trains and vehicle streams crossing the bridge are investigated in detail by the non-random vibration analysis method proposed.