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位于液体圆柱(嵌在无限介质中)内的点声源激发的轴向传播的声波。是地质和石油勘探中所常用的。本文试图对液柱内的声场进行计算,对复变函数的声势积分时,根据边界条件确定柱形等效反射系数,根据柯西定理确定积分路径,利用留数定理得出轴向传播圆锥形波,并解特征方程,以求得相速度和群速度的频散特征。用越过法,对里曼面的支点割线沿岸进行积分,得出纵波和横波侧面波、斯通利波以及简正型侧面波、共振波等。
An axially-propagating sound wave excited by a point source in a liquid cylinder (embedded in an infinite medium). Commonly used in geology and oil exploration. This paper attempts to calculate the sound field in the liquid column. For the integral of complex functions, the equivalent reflection coefficient of the column is determined according to the boundary conditions. The integral path is determined according to Cauchy’s theorem, and the axial propagation conic Wave, and solve the eigenvalue equation, in order to obtain the phase velocity and group velocity dispersion characteristics. Using the method of crossing the law, we can integrate the longitudinal and transverse waves, the Stoneley waves, the simple normal flank waves,