Research On Multiple Scattering Of Elastic Waves By Rows Of Discontinuous Barrier

The radiation propagating through medium, such as optical, electromagnetic and acoustical waves, will change its original rectilinear trajectory influenced by the obstacles embedded in the medium, and this physical process is so-called scattering. Multiple scattering theory of acoustical and electromagnetic waves have been improved sophisticatedly. However, multiple scattering in elastic waves has not ever been systematically studied so far. Artificial vibration induced by traffic loads gradually becomes one of the serious environment pollution problems influencing people’s daily work, study and life due to the rapid development of social economy and urban construction. To find out ways of reducing or even isolating vibration so that minimizing the interference of surroundings turns to be the subject needed to resolve by engineering and technicians. Setting barriers between vibration source and protected objects is an effective and commonly used reduction measure, including pile rows as the representative of discontinuous barriers. Nevertheless, theoretical solutions of pile-row as scatterers usually limit to single-row piles, regular configuration and identical cross-section; Most important, those theories of single scattering hypothesis have the shortcomings resulted from neglecting the contributions of coherent phase relations between the waves piles scatter. This multiple interaction need not to be taken into accout only if the individual scatterers are sufficiently far apart or the wavelengths are short enough. Therefore, research on multiple scattering of elastic waves by an arbitrary configuration of scatterers is not only of theoretical significance, but also of great application value in practical engineering.Based on elastic wave propagation and scattering theory, it is introduced acoustical and electromagnetic multiple scattering solution. By adopting coordinates translating approach and wave function expansion method with Fourier-Bessel series, the first-order scattering undetermined complex coefficients are obtained according to the boundary conditions.On account of the first order radiation of all others is taken to be the secondary excitation, those remaining scatterers are translated to the origin of the particular one from which the second order scattering complex coefficients are calculated as well. Thus the successive order iteration and corrections are proceeded with respect to the single scattering solution. Finally, the theoretical solution of elastic waves multiple scattering by an arbitrarily configuration and radius of scatterers is obtained.Assuming that the pile-rows are rigid so that pile materials are much stiffness than soil, which means pile-soil interface is with no displacement, it is received a theoretical derivation of arbitrarily configuration and radius pile-rows by incident of SH, P and SV waves. Numerical calculation provides the non-dimensionless curves behind barriers. Such impact parameters of vibration isolation effect on single and multi-row pile barriers are analyzed.By constructing pile-rows internal transmission field and assuming that pile-soil interface satisfies elastic displacement and stress boundary conditions, the multiple scattering and transmitted complex coefficients are solved. The total wave field solution is confirmed as well. Several numerical calculation of single and multi-row elastic piles are carried out. Those analysis results provide some instructive suggestions of engineering vibration isolation design.Replacing the solid pile-row by tubular piles, it is imposed a same transmitted wave field interior of piles. Using the multiple scattering approach of elastic waves induced above, each order of scattering and transmitted coefficients are achieved with continuity boundary conditions. A more general theoretical solution has been acquired which can be degenerated to both rigid and elastic solid pile solutions. The results of numerical example present several influencing parameters of tubular pile-rows consequentlyIt is utilized the multiple scattering method to solve the dynamic responses problem of arbitrary arrangement and radii of deep-buried cavities and linings. Several influence parameters of dynamic stress concentration on cavities and linings have been theoretically investigated with specific numerical examples.