| Dynamic response of utensils,which is taken as an evaluation index of earthquake intensity,is a normal earthquake phenomenon.Under earthquakes,rocking and collapse responses of huge utensils,i.e.,furniture and equipment,introduce massive casualties and economic losses.Therefore,dynamic problem of this kind of rigid blocks has been concerned since 1960 s when it was proposed by Housner.Especially,researches on numerical simulations and experiments of rigid blocks are gotten more concerns of domestic and overseas scholars,along with the rapid development of computation and experiment techniques recently.Rocking responses of rigid blocks involves geometrically nonlinearity and collision problems,which induces complexity to its dynamic simulations.Also the dynamic response of rigid blocks is susceptible to fabrication accuracy and elastic modulus of specimen,which causes lower repeatability of its dynamic experiment and lower consistence between numerical and experimental results.This paper takes the unanchored rigid block as the research object,and aims to study the rocking dynamic response under the pulse-like ground motion through the analysis on the rocking response theory,Matlab numerical values,small shaking table tests and influence factors of the rocking response.Focusing on dynamic analysis of rigid blocks,this thesis carries on systematic researches in terms of ground motion,dynamic equations,collision analysis,numerical algorithms,dynamic experiment,characteristics and impact of its earthquake response,etc.The main contributions and conclusions of the thesis are summarized as follows:(1)Two methods for identifying pulse-like ground motion are introduced,i.e.,one based on the wavelet analysis method and the other based on energy.The principal of ground motion selection is proposed for dynamic analysis of rigid blocks.And 10 pulse-like earthquake waves are obtained,as well as the corresponding non-pulse-like waves whose velocity pulse is eliminated by the wavelet analysis method.(2)Based on the Lagrange equation and non-slipping assumption,the rocking motion equations of symmetric,asymmetrical and irregular rigid block is derived.In addition,two collisions,including ground collision and wall collision,are studied,and the recovery coefficients of ground collision is obtained according to the conservation of angular momentum.(3)Numerical simulation programs for solving the rocking response of rigid block are compiled on Matlab platform.Three elaborate methods are proposed,the substep method,two-step method and substep-two-step method,to refine the integration around collision point.In view of Rosenbrock integration method,numerical simulation methods are developed.(4)Both numerical and experimental simulations are carried out.Through the comparison between their results,the rationalities of the proposed numerical method and the Matlab simulation program for rigid blocks are verified.(5)Based on the Matlab program,a series of numerical simulations are done to study characteristics and impact of the rocking response of the rigid blocks.It is reflected that the velocity pulse of ground motion increase the rocking response of rigid blocks under the same peak acceleration of the ground motion.And the peak rotational response of the rigid blocks is related to the peak velocity of the ground motion.Under the ground motion,the eccentricity of the rigid block usually enlarge the rocking response.Longer eccentric distance normally induces higher rocking responses as well as lower stability.Furthermore,the wall collision has a certain effect on the rocking response,which may increase its collapse probability. |
