SH波入射时非等腰三角形结构与基础相互作用
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摘要
利用复变函数和坐标移动方法研究了SH波入射时非等腰三角形结构与基础的相互作用.建立数学模型,并将模型分割为两部分,其一为非等腰三角形和半圆形组成的区域Ⅰ,其余为区域Ⅱ;在区域Ⅰ内构造一个满足非等腰三角形两边应力自由的驻波解,在区域Ⅱ内构造满足水平边界应力自由的散射波;利用"契合"思想,通过移动坐标在区域Ⅰ、Ⅱ的公共边界实现位移和应力的连续,建立求解该问题的无穷代数方程组;数值分析结果表明:入射波的物理参数对非等腰三角形结构表面位移的影响显著.结构对SH波在弹性空间传播的影响突出.较"软"的结构相对较"硬"的结构吸收"能量"较多,反射"能量"水平差,使表面位移大小及出现地点不同.
The ground motion of an scalene triangular dike impacted by SH waves is discussed.The methods of complex function and moving coordinate system as well as a simple mathematic model are used here.The model is divided into two parts,a wave function which satisfies the condition of stress free at the triangular wedges is constructed in one part,and a scattered wave function which satisfies the condition of stress free at the horizontal surface is constructed in the other part.Then the moving coordinate system is used to transform the solution of this problem into a"conjunction"problem.Finally,the solution of the problem is reduced to a series of algebraic equations and can be solved numerically.Numerical examples show that the influence of incident SH wave characters on the ground motion is great,and the influence of structure on incident SH wave is significant.Compared with stiff structures,the values of ground motion and the points where they happen for soft structures are different greatly because of their good capability of energy absorption.
The ground motion of an scalene triangular dike impacted by SH waves is discussed.The methods of complex function and moving coordinate system as well as a simple mathematic model are used here.The model is divided into two parts,a wave function which satisfies the condition of stress free at the triangular wedges is constructed in one part,and a scattered wave function which satisfies the condition of stress free at the horizontal surface is constructed in the other part.Then the moving coordinate system is used to transform the solution of this problem into a"conjunction"problem.Finally,the solution of the problem is reduced to a series of algebraic equations and can be solved numerically.Numerical examples show that the influence of incident SH wave characters on the ground motion is great,and the influence of structure on incident SH wave is significant.Compared with stiff structures,the values of ground motion and the points where they happen for soft structures are different greatly because of their good capability of energy absorption.
引文
[1]胡聿贤.地震工程学[M].北京:地震出版社,2006.
[2]申爱国.土-结构动力相互作用研究及其应用[D].大连:大连理工大学,1996.
[3]林皋,关飞.结构-地基相互作用对重力坝地震反应的影响[J].地震工程与工程振动,1991,11(4):65-76.
[4]KOJIC S,TRIFUNAC M D.Earthquake stresses in arch dams:I-theory and antiplane excitation[J].J Eng Mech,ASCE,1991,117(3):553-574.
[5]LUCO I E.Dynamic interaction of a shear wall with the soil[J].J Eng Mech,ASCE,1969,95:333-346.
[6]TRIFUNAC M D.Interaction of a shear wall with the soil for incident plane SH waves[J].Bull Seism Soe Am,1972,62:63-83.
[7]TOTOROVSKA M I,TRIFUNAC M D.Analytical mod-el for in-plane building-foundation-soil interac-tion:Incident P-SV-and Rayleigh Waves[R].los angeles,California:Dept of Civil Engrg,University of Southern California,1990:No.CE90-01.
[8]TOTOROVSKA M I,TRIFUNAC M D.The system damping,the system frequency and the system re-sponse peak amplitudes during in-plane building-soil interaction[J].Earthquake Engrg Struct Dynam,1992,21(2):127-144.
[9]邱发强,刘殿魁.SH波入射时柔性基础上等腰三角形坝体结构的出平面反应[J].地震工程与工程振动,2006,26(4):9-17.
[2]申爱国.土-结构动力相互作用研究及其应用[D].大连:大连理工大学,1996.
[3]林皋,关飞.结构-地基相互作用对重力坝地震反应的影响[J].地震工程与工程振动,1991,11(4):65-76.
[4]KOJIC S,TRIFUNAC M D.Earthquake stresses in arch dams:I-theory and antiplane excitation[J].J Eng Mech,ASCE,1991,117(3):553-574.
[5]LUCO I E.Dynamic interaction of a shear wall with the soil[J].J Eng Mech,ASCE,1969,95:333-346.
[6]TRIFUNAC M D.Interaction of a shear wall with the soil for incident plane SH waves[J].Bull Seism Soe Am,1972,62:63-83.
[7]TOTOROVSKA M I,TRIFUNAC M D.Analytical mod-el for in-plane building-foundation-soil interac-tion:Incident P-SV-and Rayleigh Waves[R].los angeles,California:Dept of Civil Engrg,University of Southern California,1990:No.CE90-01.
[8]TOTOROVSKA M I,TRIFUNAC M D.The system damping,the system frequency and the system re-sponse peak amplitudes during in-plane building-soil interaction[J].Earthquake Engrg Struct Dynam,1992,21(2):127-144.
[9]邱发强,刘殿魁.SH波入射时柔性基础上等腰三角形坝体结构的出平面反应[J].地震工程与工程振动,2006,26(4):9-17.
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