Improved Method Of Multiple Scattering Of Elastic Waves And Its Application In Engineering

Waves move at a constant speed rectilinearly in an unbounded, isotropic and homogeneous space. However, propagation of waves would be interrupted if there are some obstacles in the medium. Some secondary waves will be aroused, which is called scattering wave. Multiple scattering of elastic waves has been noticed and researched for a long time, such as vibration isolation by rows of piles and dynamic stress response of linings. Nevertheless, as far as theoretical method is concerned, all of the precedent work was focused on single-row-pile isolation system and double linings. Little work has been carried on multiple-row-pile system or response of multiple linings. This is obviously not the case in the practical engineering. Thus, it is of fatal importance to analyze these problems theoretically.Firstly, based on the analytical method of Aviles and basic theories of elastic wave, an improved expansion method of wave functions using more complete Fourier-Bessel function series has been adopted. According to Graf addition theorem which is in a more generalized perspective, formulas of scattering wave field can be expressed under one cylinder coordinate system. With the help of boundary conditions, coefficients of multiple scattering of elastic waves by an arbitrary configuration of cylinders have been deduced.Secondly, these cylinders are assumed to be rigid and rearranged in two parallel lines, which turns the problem into vibration isolation using multiple rows of rigid piles. Based on the improved method raised in this article, multiple scattering coefficients of this two-row rigid piles system under incidence of elastic waves (P, SV and SH waves) can be obtained. Then, normalized displacements (the ratio of the displacement amplitudes of soil in total wave field to the displacement amplitudes only in incident wave field) and transmissibility index (the mean value of normalized displacements across the barrier) were introduced. Detailed parametric study has been done in the following.Thirdly, these cylinders are assumed to be elastic and rearranged in two parallel lines, which turns the problems into vibration isolation under incidence of plane SV waves using multiple rows of elastic piles. Similarly, normalized displacements and transmissibility index were introduced and parametric study of this isolation system has been done through computational numeric calculation.Finally, dynamic response of deeply embedded linings under incidence of plane SH waves has been studied. Herein an arbitrary configuration of three linings was taken as an instance. According to the improved method put forward in this article and boundary conditions of linings which is the key difference with piles, scattering coefficients of multiple linings were deduced.