Dimensional Analysis Of Pounding Response Between Adjacent Structures Under Simplified Seismic Excitation

Pounding between adjacent structures is one of the main causes of structural damage,collapse and loss of property and casualties.The pounding between the adjacent structures is not only affected by the characteristics of ground motion,but also related to the characteristic of the adjacent structures,which is a highly nonlinear problem involving a large variety of parameters.And the large number of influencing parameters firstly increases the difficulty of the research,and secondly,will cause the research results to be one-sided instead of universal.In this case,the dimensional analysis method can be used to study the pounding response with less dimensionless parameters,which can more clearly reflects the law of the collision reaction of the adjacent structures under earthquakes.In addition,due to the limitations of the commonly used pounding models,it is extremely important to simulate the collision process by using a suitable pounding model for pounding studies between adjacent structures under earthquakes.Therefore,combined the dimensional analysis with the modified Kelvin impact analytical pounding model,this paper investigates the pounding response of an elastic oscillator and rigid barrier,two inelastic single freedom structures and two inelastic multi-degree-of-freedom structures.The main contents and the conclusions of this study by using theoretical and numerical analysis are as follows:(1)The pounding responses between the oscillator and the rigid barrier are investigated with the dimensional analysis method.The dimensionless equation of motion of the single pounding oscillator and the dimensionless pounding force are deduced.Through numerical analysis,the dimensionless pounding responses of the oscillator based on the modified Kelvin pounding analytical model are compared with the responses based on the Kelvin pounding analytical model,which proves the superiority of the modified Kelvin model.Besides,the effects of pounding on the response of the oscillator are illustrated using three well-separated spectral regions(i.e.,amplified region,hindered region and unaffected region)and the self-similarity is proved.Finally the influence of the contact element parameters on the collision response is studied.It is found that the contact stiffness and the initial spacing have little effect on the pounding response,while the recovery coefficient has a great influence on the pounding response.(2)The pounding responses between two inelastic SDOF structures are investigated with the dimensional analysis method.The dimensionless equation of motion of two inelastic SDOF structures and the dimensionless pounding force are deduced.Beside,the effects of pounding on the response of the inelastic structure which is lighter and flexible are illustrated using three well-separated spectral regions(i.e.,amplified region,hindered region and unaffected region)and the self-similarity is proved.Finally the influence of the structural parameters on pounding response is studied.It is found that the influence on pounding response of the mass ratio,frequency ratio and initial spacing for the left structure(lighter and flexible)have a close relationship with the three spectral regions.For the right structure(heavier and stiffer),the amplification of pounding gradually increases with the increasing of the mass ratio,and decreases with the increasing of the frequency ratio and the initial spacing.(3)The pounding responses between two inelastic MDOF structures are investigated with the dimensional analysis method.The dimensionless equation of motion of two inelastic MDOF structures and the dimensionless pounding force are deduced.Compared the dimensional and dimensionless pounding responses of two inelastic MDOF structures under different excitation acceleration amplitudes,the self-similarity of two inelastic MDOF structure is proved.Furthermore,shaking table tests of adjacent steel frame structures are carried out.By comparing the experimental results with the numerical results obtained by using MATLAB programming,the rationality of the numerical simulation methods and the results are proved.Beside,the pounding influence on the structural response is divided into three regions,and the influence of story mass ratio,post-yielding stiffness ratio,yield displacement and initial spacing on the collision response is analyzed.