Scattering of SH-wave by multiple circular cavities in half space

In this paper,an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space.The scattered wave function used for scattering of SH-waves by multiple circular cavities,which automatically satisfies the stress-free condition at the horizontal surface,is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system.Applying this scattered wave function and method of moving coordinates,the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space.Finally,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones.Numerical examples are provided for case with two cavities to show the effect of wave number,and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

On acoustic performance for viscoelastic coating containing axisymmetric cavities using the multiple scattering method

A semi-analytical/numerical model based on the multiple scattering （MS） method has been established for analyzing the effect of acoustic performance on main energy attenua- tion mechanism in viscoelastic coating containing axisymmetric cavities. The basic functions of stress and displacement of the axisymmetric cavity surface are derived in the system of spheri- cal coordinates. The transition matrix between the incident wave and the scattering wave are obtained by the numerical integral of the basic functions of the cavity surface. The reflection, transmission and absorption performance of viscoelastic materials containing periodic cavities are calculated using the MS method and the wave propagating theory of the multi-layered medium. The results indicate that low frequency energy is mainly attenuated through cavity resonance. The resonant properties are found to be very sensitive to the boundary conditions. The coupling of the double-cavity is capable of extending the absorption to even lower fre- quencies. The absorption performance of the viscoelastic coating in the high frequency range is independent of the backing material. Its energy attenuation depends mainly on acoustic properties of cavity scattering and mode conversion.