AN ANALYTICAL SOLUTION FOR WAVE PRESSURE ON ARRAYS OF ELLIPTICAL BODIES

In an array of elliptical cylinders, upon impinging on large structure, linear incident waves are scattered by bodies; the scattered waves due to linear incident waves subsequently impinge other bodies; the higher-order scattered waves are generated in the same manner as the multiple scattering problem exists. Based on the diffraction theory and elliptic cylindrical coordinates, the analytical solution for the incident and the scattered waves, say the first-order scattered wave, on an isolated elliptical body is formulated firstly; then, with the first-order scattered wave from other bodies as the excitation source, the analytical solution for second-order scattered waves is developed; Analogously, the analytical solution for higher-order scattered waves is obtained; finally, the total wave pressure on a body in an array is obtained in a form of a sum of the incident wave pressure, the first-order scattered wave pressure due to the linear incident wave and the scattered wave pressure considering multiple scattering waves. The present method is validated by a FEM and is applied to two cases in which multiple scattering problem on bodies with different parameters (wave number, separation, wave propagation direction, etc.) is discussed. It can be seen from the results that the effect of high-order scattered wave matters as the wave number is large; multiple scattering problem is reducing but still exists as the distance between bodies increasing; As the quantity of bodies growing, the multiple scattering problem is increasing and its impact is drastically undulant; the effect of high-order scattered wave on the leading structures is larger than that on the one in the downstream.