爆炸荷载作用下地下拱结构动力分析
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摘要
为了准确分析爆炸作用下地下拱结构的动力响应,利用阻尼系数来表达土介质与结构的动力相互作用,建立结构运动方程。由于结构动态响应方程的复杂性,在计算中对结构进行了简化,忽略了结构剪切力、转动惯性矩以及切向力的影响,并且假设拱结构在切线方向是不可延展的。利用振型分解法获得了两端固支拱结构在爆炸荷载作用下的动态响应的解析解。对圆心角为120°的拱结构单元进行了计算,得出了位移、速度和加速度时程响应曲线,探讨了参数响应的最大值与比例爆距之间的关系,得到了最大值与比例爆距之间的关系曲线。利用解析计算得到了结构弯矩的包络图。
An exact solution for the vibration of arches subject to forces of denotation is obtained by employing a modal superposition method.As to the complicities of the problems of an arch,some simplifications are made,such as the effect of shear,rotary inertia and tangential forces are neglected and the arch is supposed to be incompressible.In order to simulate the forces applied on the underground structure,the soil-structure interaction is considered using a damping coefficient.An arch element with an opening angle of 120° is used for calculating and the responses of displacements,velocities and accelerations are obtained.The relation between the maximum response and the scaled distance is analyzed and the figure is plotted.According to the suggested method,maximum internal forces of each cross section of the arch can be calculated.
An exact solution for the vibration of arches subject to forces of denotation is obtained by employing a modal superposition method.As to the complicities of the problems of an arch,some simplifications are made,such as the effect of shear,rotary inertia and tangential forces are neglected and the arch is supposed to be incompressible.In order to simulate the forces applied on the underground structure,the soil-structure interaction is considered using a damping coefficient.An arch element with an opening angle of 120° is used for calculating and the responses of displacements,velocities and accelerations are obtained.The relation between the maximum response and the scaled distance is analyzed and the figure is plotted.According to the suggested method,maximum internal forces of each cross section of the arch can be calculated.
引文
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[2]Kang K J,Bert C W,Striz A G.Vibration and bucklinganalysis of circular arches using DQM[J].Computersand Structures,1996,60(1):49―57.
[3]Chidamparam P,Leissa A W.Influence of centerlineextensibility on the in-plane free vibrations of loadedcircular arches[J].Journal of Sound and Vibration,1995,183(5):779―795.
[4]Matsunaga H.In-plane vibration and stability of shallowcircular arches subjected to axial forces[J].InternationalJournal of Solids and Structures,1996,33(4):469―482.
[5]吴玉华,楼文娟.水平随机地震激励下弹性圆拱的半解析法[J].浙江大学学报(工学版),2010,44(11):156―159.Wu Yuhua,Lou Wenjuan.Semi-analytical solution ofelastic circular arch under horizontal random seismicexcitation[J].Journal of Zhejiang University(Engineering Science),2010,44(11):156―159.(inChinese)
[6]Henrych J.The dynamics of arches and frames[M].Amsterdam:Elsevier,1981:104―105.
[7]US Army Engineers Waterways Experimental Station.Fundamentals of protective design for conventionalweapons[S].TM5-855-1,Vicksburg,1986.
[8]Weidlinger P,Hinman E.Analysis of undergroundprotective structures[J].Journal of StructuralEngineering,ASCE,1988,114(7):1658―1673.
[9]Wong F S,Weidlinger P.Design of undergroundprotective structures[J].Journal of StructuralEngineering,ASCE,1983,109(8):1972―1979.
[10]Ma G W,Zhou H Y,Lu Y,Chong K.In-structure shockof underground structures:A theoretical approach[J].Engineering Structures,2010,32:3836―3844.
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