Based on the period feature of the dispersion equation,the approximate formulas of the average interval of period-modes curves and also the number of roots(i.e.the number of multimodes) at any frequency and velocity are presented.
The elements of transfer matrix T of the displacement stress vector is written with real and dimensionless quantities, to improve the speed and stability of the computation and discover the relationship of some algorithms and it is then discovered that plane Rayleigh wave and cylindrical Rayleigh wave have exactly the same dispersion equation.
为了提高计算的速度和稳定性以及发现不同算法之间的联系 ,将位移应力矢量的传递矩阵 T 的元素表示为实数量及无量纲量的形式 ,发现柱面瑞雷面波与平面瑞雷面波的频散方程形式可以完全一样 ;
Synthesizing three major factors of half-space multilayer media, namely elasticity. viscosity and anisotropy, the present paper, using finite element method, established the surface wave frequency divergent equation for this sort of complex media model, and analysed main characteristics of the frequency divergent equation.
The velocity of immersion Rayleigh waves has been theoretically calculated and experimentally measured according to the dispersive equation of half-infinite medium with a liquid layer. Quantitative agreement has been obtained between theory and experiment.
The frequency dispersive equation of Rayleigh wave with a solid layer is at first derived, then with proper mathematic treatment, the equation can be easily transfered to such frequency dispersive equations of Rayleigh waves as with a solid layer, or with a viscous fluid layer, or with a no-viscious fluid layer or with relative half-infinity layers.
The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field.
The dispersion equation obtained, determining the velocity of five types of waves, is analyzed.
The equilibrium state of thin liquid films with account for the Van der Waals forces is considered and the dispersion equation for the capillary-Van der Waals surface waves is obtained.
The dispersion equation for the capillary oscillations of a charged drop of viscous incompressible fluid of finite electrical conductivity with account for energy loss by electromagnetic-wave radiation is obtained.
Solutions of the dispersion equation are given for all positions of the emitting surface (arbitrary, vertical, horizontal, and critical when one of the beam propagation directions is collinear with the emitting surface).