土-结构相互作用系统地震动力特性的突变理论分析
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摘要
地震荷载作用下,将土和结构作为一个系统,可较好体现地震作用下结构动力特性的影响.对一个简单的土-结构相互作用系统模型,计算了其动能和形变能,通过拉格朗日方程导得对土-结构相互作用系统的运动方程,并将其归结为以结构振幅为状态变量的尖点突变模型,来对结构的动力特性进行分析.尖点突变模型的对应性状表明,非线性弹簧使系统具有可变频特性,使得地震作用下的土-结构相互作用系统不发生线性系统中的"共振"现象;当系统频率变化使控制点(u,v)跨越尖点突变模型分叉集时,结构的振幅和振动相位会发生突变,并且结构振幅的突变值随地震频率而变,也即地震频率变化对土-结构相互作用系统动力特性的影响有"路径"效应.
Under earthquake loading,the dynamic characteristics of structure can be reflected better when soil and structure are analyzed by a system.On a simple model of soil-structure interaction system,the kinetic energy and deformation energy are calculated.The dynamic equations of soil-structure interaction system derived by Lagrange Equation can be attributed to the cusp catastrophe model which takes structure amplitude as state variable.The analysis by cusp Catastrophe Theory shows that because of nonlinear spring,the system has the frequency characteristics and the soil-structure interaction system does not produce a "resonance" phenomenon in linear systems.When the control points(u,v) get across the bifurcation set of cusp catastrophe model,structure amplitude and vibration phase will change and the structure amplitude changes with the earthquake frequency,i.e.the earthquake frequency change has path effect on earthquake dynamic characteristics of soil-structure interaction system.
Under earthquake loading,the dynamic characteristics of structure can be reflected better when soil and structure are analyzed by a system.On a simple model of soil-structure interaction system,the kinetic energy and deformation energy are calculated.The dynamic equations of soil-structure interaction system derived by Lagrange Equation can be attributed to the cusp catastrophe model which takes structure amplitude as state variable.The analysis by cusp Catastrophe Theory shows that because of nonlinear spring,the system has the frequency characteristics and the soil-structure interaction system does not produce a "resonance" phenomenon in linear systems.When the control points(u,v) get across the bifurcation set of cusp catastrophe model,structure amplitude and vibration phase will change and the structure amplitude changes with the earthquake frequency,i.e.the earthquake frequency change has path effect on earthquake dynamic characteristics of soil-structure interaction system.
引文
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