解放军理工大学学报(自然科学版)
解放軍理工大學學報(自然科學版)
해방군리공대학학보(자연과학판)
JOURNAL OF PLA UNIVERSITY OF SCIENCE AND TECHNOLOGY(NATURAL SCIENCE EDITION)
2014年
6期
558-563
,共6页
张进凡%戚承志%潘越峰%徐琛%刘旭
張進凡%慼承誌%潘越峰%徐琛%劉旭
장진범%척승지%반월봉%서침%류욱
土层自由场%水平维度%衰减%相对位移
土層自由場%水平維度%衰減%相對位移
토층자유장%수평유도%쇠감%상대위이
free field soil%horizontal dimension%attenuation%relative displacement
为了研究均匀土层自由场地震动的二维简化模型,首先利用弹性波动理论,得到土介质的二维波动方程,采用分离变量法来求解该方程,根据土层上下界面的边界条件确定土层竖向振动的特征频率和振型;根据波沿水平方向向无穷远处传播的衰减特性确定波沿水平方向衰减系数,得到土层自由场自由振动的相对位移的解析解。然后,采用振型叠加法求解强迫振动情况下的波动方程,得出二维情况下均匀土层在地震作用下沿水平方向相对位移的解析解。通过上述计算,得到了土层自由场地震动的二维简化模型。通过具体算例,分别对研究的二维简化模型与一维剪切梁模型进行了比较。比较结果表明,地下土层水平维度对于均匀土层自由场地震动反应的影响很小。
為瞭研究均勻土層自由場地震動的二維簡化模型,首先利用彈性波動理論,得到土介質的二維波動方程,採用分離變量法來求解該方程,根據土層上下界麵的邊界條件確定土層豎嚮振動的特徵頻率和振型;根據波沿水平方嚮嚮無窮遠處傳播的衰減特性確定波沿水平方嚮衰減繫數,得到土層自由場自由振動的相對位移的解析解。然後,採用振型疊加法求解彊迫振動情況下的波動方程,得齣二維情況下均勻土層在地震作用下沿水平方嚮相對位移的解析解。通過上述計算,得到瞭土層自由場地震動的二維簡化模型。通過具體算例,分彆對研究的二維簡化模型與一維剪切樑模型進行瞭比較。比較結果錶明,地下土層水平維度對于均勻土層自由場地震動反應的影響很小。
위료연구균균토층자유장지진동적이유간화모형,수선이용탄성파동이론,득도토개질적이유파동방정,채용분리변량법래구해해방정,근거토층상하계면적변계조건학정토층수향진동적특정빈솔화진형;근거파연수평방향향무궁원처전파적쇠감특성학정파연수평방향쇠감계수,득도토층자유장자유진동적상대위이적해석해。연후,채용진형첩가법구해강박진동정황하적파동방정,득출이유정황하균균토층재지진작용하연수평방향상대위이적해석해。통과상술계산,득도료토층자유장지진동적이유간화모형。통과구체산례,분별대연구적이유간화모형여일유전절량모형진행료비교。비교결과표명,지하토층수평유도대우균균토층자유장지진동반응적영향흔소。
The simplified 2-D model for determination of free field seismic motion of uniform soil strata was studied. Firstly, the two-dimensional wave equation of the soil was obtained with the theory of elastic wave. The method of separation of variables was used to solve the equation. The natural frequencies and mode shapes of vertical vibration of soil were determined by using the boundary conditions of the upper and lower soil interface. According to the wave attenuation properties of wave propagation to infinity,the wave attenuation coefficient along the horizontal di-rection was determined, and the relative displacement analytical solution of free vibration was obtained. Then the forced vibration equation was solved by using the mode superposition method. As a result, the analytical solution of the horizontal relative soil displacement was obtained. Through the above calculations, the simplified 2-D model for determination of free field seismic motion of soil strata was obtained. Finally, the 2-D model was compared with the 1-D shear beam model,and the results show that the horizontal dimension has little effect on the seismic response of the soil.