SWT方法在内部充水弹性球壳散射的应用

采用Sommerfeld-Watson变换(SWT)方法研究了内部充水弹性球壳的散射,应用绕数积分求根方法在频率域复平面和波数域复平面求解环绕波的频散方程。比较了弹性球壳在内部真空和内部充水两种情况下环绕波相速度曲线和衰减曲线,结果表明内部流体负载使得相对于内部真空情况有大量流体环绕波产生,相邻流体环绕波相速度曲线的"排斥"现象是明显的,流体波向周围媒质的再辐射作用在其相速度接近内部真空球壳弹性环绕波相速度的时候达到局部极值。用镜反射波和环绕波的叠加合成反向散射形态函数,与简正级数解符合良好。

Application of the SWT Method to Scattering from Water-filled Elastic Spherical Shells

The method of Sommerfeld-Watson Transformation (SWT) is completely applied to scattering from a water-filled elastic spherical shell.Dispersion equations in the frequency domain and the wave number domain are numerically solved using winding integral method. A comparison of phase velocity as well as attenuation curves of corresponding circumferential waves for water-filled and evacuated spherical shell is presented. Analysis of the water-filled spherical shell suggests that there are many fluid waves occurred due to internal fluid loading, the repulsion phenomenon of phase velocity curves for adjacent fluid waves is obvious and the ability of the fluid wave re-radiation to the surrounding medium is reaching local extremum when the phase velocity of fluid wave for the water-filled shell is close to that of elastic waves for the evacuated shell. Numerical results validate the SWT method and show that the SWT synthesis of backscattering form function which is the sum of specular reflection part and circumferential waves agrees with the partial wave series approach.