三维层状黏弹性半空间中球面SH、P和SV波源自由场

发布时间：2018-11-12 13:03

【摘要】：采用刚度矩阵方法结合Hankel积分变换,求解了层状黏弹性半空间中球面SH、P和SV波的自由波场.首先,在柱坐标系下建立层状黏弹性半空间的反轴对称(柱面SH波)和轴对称(柱面P-SV波)情况精确动力刚度矩阵.进而由Hankel变换将空间域内的球面波展开为波数域内柱面波的叠加,然后将球面波源所在层的上下端面固定,求得固定层内的动力响应和固定端面反力,将固端反力反向施加到层状黏弹性半空间上,采用直接刚度法求得固端反力的动力响应,叠加固定层内和固端反力动力响应,求得波数域内球面波源动力响应.最后由Hankel积分逆变换求得频率-空间域内球面波源自由场,时域结果由傅里叶逆变换求得.文中验证了方法的正确性,并以均匀半空间和基岩上单一土层中球面SH、P和SV波为例分别在频域和时域内进行了数值计算分析.研究表明基岩上单一土层中球面波自由场与均匀半空间情况有着本质差异;基岩上单一土层中球面波位移频谱峰值频率与场地固有频率相对应,基岩面的存在使得基岩上单一土层地表点的位移时程非常复杂,振动持续时间明显增长;阻尼的增大显著降低了动力响应的峰值,同时也显著减少了波在土层的往复次数.
[Abstract]:The free wave fields of spherical SH,P and SV waves in layered viscoelastic half-space are solved by using stiffness matrix method and Hankel integral transformation. Firstly, the exact dynamic stiffness matrices of anti-axisymmetric (cylindrical SH wave) and axisymmetric (cylindrical P-SV wave) in layered viscoelastic half-space are established in cylindrical coordinate system. Then the spherical wave in the space domain is expanded into the superposition of the cylindrical wave in the wavenumber domain by Hankel transform, and then the upper and lower end surfaces of the layer in which the spherical wave source is located are fixed, and the dynamic response and the reaction force of the fixed end surface in the fixed layer are obtained. The fixed end reaction force is applied to the layered viscoelastic half-space, and the dynamic response of the fixed end reaction force is obtained by using the direct stiffness method, and the dynamic response of the spherical wave source in the wavenumber domain is obtained by superposing the dynamic response of the fixed layer and the fixed end reaction force. Finally, the free field of spherical wave source in frequency-space domain is obtained by Hankel integral inversion, and the time domain result is obtained by inverse Fourier transform. The correctness of the method is verified and numerical analysis of spherical SH,P and SV waves in homogeneous half-space and single soil layer is carried out in frequency domain and time domain respectively. The results show that there are essential differences between the free field of spherical wave and the homogeneous half-space in the single soil layer on the bedrock. The peak frequency of the displacement spectrum of spherical wave in the single soil layer corresponds to the natural frequency of the site. The existence of the bedrock surface makes the displacement time history of the surface point of the single soil layer on the bedrock very complex and the vibration duration obviously increasing. The increase of damping decreases the peak value of dynamic response and the number of waves reciprocating in the soil.
【作者单位】：天津大学土木系;滨海土木工程结构与安全教育部重点实验室;
【基金】：国家自然科学基金(51578373;51578372) 天津市应用基础及前沿技术研究计划(12JCQNJC04700)资助
【分类号】：P315.3

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