Impact Models And Experimental Studies Of Repeated Impacts On Elastic-Plastic Beams

Repeated impact is a ubiquitous phenomenon in engineering,where the mechanical behaviors are more complicated than single impact.Repeated impact on flexible structures involves structural response,wave propagation and local impact behaviors.Investigations have found that even for low velocity impact,high stresses can be initiated in the contact area which exceed the yield stress of the material.Therefore,plastic deformation happens during impact.Various contact models have been proposed in order to study the local contact behaviors of single impact.In order to simulate the structural response and the wave propagation of single impact problems,many methods also have been proposed to analyse the dynamic response of impact on structures.There are less methods for analysing contact behaviors and structural responses of repeated impacts.The typical way to analyse repeated impacts is to modify the analysing methods for single impact and then the modified methods are used to analyse the repeated impacts.However,the application and the accuracy of using these methods are short of research.This dissertation choses the repeated impacts between a steel sphere and an elastic-plastic beam as the research object.By using the theoretical and experimental methods,the different contact models and methods for analysing structural responses are compared.The main research contents are summarized as follows:(1)The widely used elastic-plastic contact models are aanlyzed and summarized.According to the divisions of contact phases,the analysis methods and the contact force-indentation relationships are built.The widely used contact models are classified,and the repeated loading phases are added to study the repeated impact problems.(2)By using an experimental setup for repeated impacts,the repeated impact behaviors of a steel sphere on an elastic-plastic beam are studied.The contact time,the separation velocity of the sphere,the residual plastic deformation,the coefficient of restitution and the stress response are investigated in detail and the experimental rules of repeated impact responses are obtained.(3)By using the effective loading stiffness and unloading stiffnes,the linearization method for repeated contact are proposed.The linearized method can be used to linearize contact models,which can be combined with the two degree of freedom spring-mass model to obtain the analytical solution for repeated impacts of flexible structures.The validity of this method can be checked by using experimental method.(4)To investigate the influence of higher vibration modes and wave propagation during repeated impacts,the theoretical solution for repeated central impact response of an elastic-plastic beam has been derived by using the transient wave expansion method and a contact model.The validity of the theoretical solution,the influence of higher vibration modes and wave propagation are studied by comparing with experimental results.(5)Five methods to analyse structural response of repeated impact,i.e.the effective spring-mass method,the effective spring-mass-damper method,the approximate integral method,the modal superposition method and the transient wave expansion method,are used to analyse the repeated impacts of elastic-plasti beams,and the results are compared.By comparing with the experimental results,the wave propagations are found have slight influence on predicting the contact time,therefore the effective spring-mass method can be used to simulate the contact time.The wave propagations are found have strong influence on impact responses related energy dissipations,such as the residual plastic deformation,the separation velocity of the sphere and the coefficient of restitution,therefore the approximate integral method,the modal superposition method or the transient wave expansion method is needed.(6)Six contact models combining the approximate integral method for structural response are used to analyse the repeated impacts of an elastic-plastic beam.The comparison with experimental results show that the contact models can be used on on repeated impacts of elastic-plastic beams.Moreover,the differences of different contact models on predicting the repeated impact are found and one certain contact model cannot be used to predict accurately all of the impact responses.(7)Twenty contact models and a finite model are used to simulate the impact problem of elastic-plastic half-space,and the reasons for different predictions of impact response are analysed.The comparison results show that the different predictions are related to two parameters of contact model.These are the yield indentation for plastic deformation and the effective radius during unloading phase.The predictions of contact models have linear correlations when reasonable combined parameters are built by using these two parameters.