关于非线性水声波的近似色散关系分析
Study on Approximate Dispersion Relation of Nonlinear Hydroacoustic Wave

目前在非线性水声波的研究中，为了简化计算通常假设色散关系是线性的。然而线性色散关系式对大振幅波是不恰当的。为此，本文研究了弹性板覆盖下的有限深可压单层流体中非线性水声波的色散关系。假设流体是无粘、可压缩的，且流动是无旋的。我们构建了控制方程和表示水动力、弹性力和惯性力之间关系的边界条件，并得到水声波的一种近似非线性色散关系，对水声波模态的特性进行分析，讨论了弹性板厚度等重要物理因素对波动传播特性的影响。该研究为极地海洋资源探测、水下目标探测、海底地震和海啸预警等工程实际问题提供了理论参考。
Currently, in the research of nonlinear hydroacoustic waves, it is commonly assumed that the dispersion relation is linear in order to simplify calculations. However, the linear dispersion relation is not suitable for large-amplitude waves. So, this study investigates the dispersion relation of nonlinear hydroacoustic waves in a finite depth compressible single-layer fluid covered by an elastic plate. The fluid is assumed to be inviscid, compressible, and irrotational. We construct the governing equations and boundary conditions that represent the relationships between hydrodynamic, elastic, and inertial forces, and obtain an approximate nonlinear dispersion relation for hydroacoustic waves. The characteristics of hydroacoustic wave modes are analyzed, and the effects of important physical factors such as the thickness of the elastic plate on wave propagation properties are discussed. This research provides theoretical references for engineering practical problems such as polar marine resource detection, underwater target detection, seafloor seismic and tsunami warning.