地下管线弹性波探测波场的建模与分析

在地下管线弹性波探测中，由位于地下圆孔边界上有限时长的力源激发形成瞬态场，应用波函数展开法对此波场进行建模。以波函数和待定系数组成的级数序列描述探测波场中的势函数，根据界面处应力和位移连续的边界条件求解待定系数，从而得到波场中弹性波的解析解。据此进行数值研究，分析探测波场中弹性波的传播特征，说明了散射波的类型以及能量对比关系，并总结了反射信号幅值与地下管线物理参数之间由声阻抗匹配程度支配的反射信号强度变化规律，而管线半径对反射信号强度的影响要大于物理参数的作用。最后以实验结果验证上述结论。

An analytical model of elastic waves in detection of underground pipes

Elastic waves are excited by the linear impact force with several periods at the boundary of the underground cylindrical cavity to detect underground cylindrical pipes. It is a transient acoustic field. Based on wave functions expansion method, the waves in the field are expressed in terms of wave potentials and expanded in Fourier-Bessel series, and the coefficients in the wave functions are determined to satisfy the boundary conditions. Thus, the analytical solutions of the potential functions of the field are obtained. Then the numerical results present the waves propagating process and the relationships of energy. Furthermore, the amplitude of the reflected signals is influenced by the material parameters of the pipes; and the results are determined by the matching raw of acoustic impedance. These conclusions and experimental results are in good agreement.