基于多模态展开的黏弹性材料复纵波波速反演方法

Inversion method of complex longitudinal wave velocity of viscoelastic material based on multi-modal decomposition

黏弹性材料广泛应用于水下航行器的降噪、减振或消声,精确获取其动力学参数的需求随着数值仿真技术发展而迅速提升。针对参数获取的声管测量方式,提出了一种使用复反射系数对黏弹性材料复纵波波速快速反演的方法。通过引入多模态展开方法,将复纵波波数超越方程的复平面搜根问题转化为展开系数系统矩阵特征值分解问题,推导出了三种典型背衬情况下展开系数系统矩阵,并分析了多模态展开截断阶次和复反射系数测量误差对复纵波波速反演精度的影响。数值仿真表明,该方法可以快速、准确地反演黏弹性材料的复纵波波速。

Viscoelastic materials are widely used for noise reduction, vibration reduction or noise elimination of un- derwater vehicles. With the development of numerical simulation techniques, the demand of accurately obtaining their dynamic parameters increases rapidly. Aiming at the acoustic tube measurement method, a fast inversion method of complex longitudinal wave velocity of viscoelastic materials based on complex reflection coefficient is proposed in this paper. By introducing the multi-modal decomposition method, the complex plane root search problem of complex lon- gitudinal wave number transcendental equations is transformed into eigenvalue decomposition problem of expansion coefficient system matrix, and the expansion coefficient system matrix under three typical backing situations is derived. The influences of the multi-modal expansion truncation order and the measurement error of complex reflection coeffi- cient on the accuracy of complex longitudinal wave velocity inversion are analyzed. Numerical simulations show that this method can quickly and accurately invert the complex longitudinal wave velocity of viscoelastic materials.