Abstract：Based on the Betti-Rayleigh dynamic reciprocal theorem，the reciprocal property of the Green function is demonstrated；and the analytical solution of soil vibration subjected to moving loads is deduced. By means of double Fourier integral transform，the problem is firstly transformed into wave number-frequency domain，which makes it very convenient to derive the solution and furthermore to analyze the frequency characteristics of soil vibration. By successful application of the dynamic reciprocal theorem，the moving source problem is converted to the fixed source problem with receiver point moving in opposite direction，which greatly simplifies the complex analytical solution of soil/ground vibration induced by a moving load. A computer code for solving the ground responses subjected to the constant moving load and harmonic moving load is developed by using Matlab and is employed to perform a case study. The analytical results show that，for the constant moving load，the ground vibration is of typical low-frequency feature；while for the harmonic moving load，the frequency range of ground vibration is controlled by the Rayleigh wave velocity of the top layer soil；moreover，the Doppler effect appears in the ground vibrations. When the receiver is near the source path，R-wave contributes to ground vibration much more than P- and S-wave；while the receiver is far from the source path，the contribution of P-wave is more obvious.
曹艳梅，夏禾. 基于Betti-Rayleigh动力互易定理求解移动荷载引起的地基土振动[J]. 岩石力学与工程学报, 2009, 28(07): 1467-1476.
CAO Yanmei，XIA He. SOLUTION OF FOUNDATION SOIL VIBRATIONS INDUCED BY MOVING LOADS BASED ON BETTI-RAYLEIGH DYNAMIC RECIPROCAL THEOREM. , 2009, 28(07): 1467-1476.
