反平面冲击荷载作用下圆柱形洞室的动力响应
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摘要
对无限弹性土体内圆柱形洞室在反平面冲击荷载的作用下的瞬态响应进行了探讨。用残余变量的方法结合拉普拉斯变换及其逆变换,在频域内的得到土体位移和应力一般表达式,并采用拉普拉斯逆变换的数值方法,给出了问题的数值解。在时域内分析了无限弹性土体内圆柱形孔洞在沿轴向方向的冲击荷载作用下的土体动力响应的变化规律,并将计算结果与静力情况下的计算值作了比较:反平面荷载作用后,波向外发散传播,并沿半径方向衰减,衰减速度较静力情况下的衰减要慢,且距离波源越远二者差别越大;波到达后,该点土体的应力和位移均发生与外荷载相同的三角形变化:先增大,随后减小最后保持为零不变。
The transient response to an anti-plane impact load of an infinite elastic soil body containing a cylindrical cavity was studied.Using the residual variable method combined with Laplace transformation and its inverse transformation,the general expressions of the displacement and stress of the soil were obtained in frequency domain,respectively.And the numerical solutions were calculated by using the numerical method of inverse Laplace transformation.In time domain,the dynamic responses of a cylindrical cavity in the infinite elastic soil were analyzed under axial impact load,and the calculation results were compared with those in the static case.It was shown that after an anti-plane impact load is exerted on,the wave spreads outward,and dissipates along the radial direction;the attenuation rate is smaller than that under static conditions;and the farther the wave from its source,the greater the difference between the two rates;after wave arrivals,the stress and displacement of the soil at this point reveal triangular changes,the same as the external load,they increase at first and then decrease,and remain zero finally.
The transient response to an anti-plane impact load of an infinite elastic soil body containing a cylindrical cavity was studied.Using the residual variable method combined with Laplace transformation and its inverse transformation,the general expressions of the displacement and stress of the soil were obtained in frequency domain,respectively.And the numerical solutions were calculated by using the numerical method of inverse Laplace transformation.In time domain,the dynamic responses of a cylindrical cavity in the infinite elastic soil were analyzed under axial impact load,and the calculation results were compared with those in the static case.It was shown that after an anti-plane impact load is exerted on,the wave spreads outward,and dissipates along the radial direction;the attenuation rate is smaller than that under static conditions;and the farther the wave from its source,the greater the difference between the two rates;after wave arrivals,the stress and displacement of the soil at this point reveal triangular changes,the same as the external load,they increase at first and then decrease,and remain zero finally.
引文
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[10]蔡袁强,陈成振,孙宏磊.黏弹性饱和土中隧道在爆炸荷载作用下的动力响应[J].浙江大学学报(工学版),2011,45(9):1657-1663.CAI Yuan-qiang,CHEN Cheng-zhen,SUN Hong-lei.Dynamic response of tunnel in viscoelastic saturated soil subjected to blast loads[J].Journal of Zhejiang University(Engineering Science),2011,45(9):1657-1663.
[11]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].Crane and Russake,New York,1973:114-124.
[12]Durbin F.Numerical inversion of laplace transformation:An efficient improvement to Durbin and Abatep's method[J].The Computer Journal,1974,17(4):371-376.
[2]Forrestal M J,Sagartz M J.Radiated pressure in an acousticmedium produced by pulsed cylindrical and spherical shells[J].AMSE Journal of Applied Mechanics,1971.93:1057-1060.
[3]Akkas N.,Erdogan F..The residual variable method appliedto the diffusion equation in cylindrical coordinates[J].ACTAMechanic,1989,79:207-219.
[4]张庆元,战人瑞.爆轰载荷作用下球形空腔的动力响应[J].爆炸与冲击,1994.14(2):182-185.ZHANG Qing-yuan,ZHAN Ren-rui.Dynamic response of aspherical cavity subjected to blast loads[J].Explosion andShock Wave,1994.14(2):182-185.
[5]刘国利,赵会滨,许贻燕.阶跃SH波作用下半圆形凹陷地形的瞬态反应—长期解[J].地震工程与工程振动,1995,15(1):92-99.LIU Guo-li,ZHAO Hui-bin,XU Yi-yan.Transient responseof semi-circular canyon under step SH-wave-long-termsolution[J].Earthquake Engineering and EngineeringVibration,1995,15(1):92-99.
[6]杨峻,宫全美,吴世明,等.饱和土体中圆柱形孔洞的动力分析[J].上海力学,1996,17(1):37-45.YANG Jun,GONG Qun-mei,WU Shi-ming,et al.Dynamicanalysis of cylindrical holes in saturated soil[J].ShanghaiMechanics,1996,17(1):37-45.
[7]Zakout U,Akkas N.Transient response of a cylindrical cavitywith and without a bonded shell in an infinite elastic medium[J].International Journal of Engineering Science,1997,19(5):1341-1352.
[8]M anolis G D.Elastic wave scattering around cavities ininhomogeneous continua by the BEM[J].Journal of Soundand Vibration,2003,266:281-305.
[9]高盟,高广运,王滢,等.内部荷载作用下圆柱形孔洞的动力响应解答[J].力学季刊,2009(2):266-272.GAO Meng,GAO Guang-yun,WANG Ying,et al.Solution on dynamic response of a Cylindrical cavity under internal load[J].Chinese Qarterly of Mechanics,2009(2):266-272.
[10]蔡袁强,陈成振,孙宏磊.黏弹性饱和土中隧道在爆炸荷载作用下的动力响应[J].浙江大学学报(工学版),2011,45(9):1657-1663.CAI Yuan-qiang,CHEN Cheng-zhen,SUN Hong-lei.Dynamic response of tunnel in viscoelastic saturated soil subjected to blast loads[J].Journal of Zhejiang University(Engineering Science),2011,45(9):1657-1663.
[11]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].Crane and Russake,New York,1973:114-124.
[12]Durbin F.Numerical inversion of laplace transformation:An efficient improvement to Durbin and Abatep's method[J].The Computer Journal,1974,17(4):371-376.