Analysis on multiple scattering by an arbitrary configuration of piles as barriers for vibration isolation

By introducing the multiple scattering of acoustic or electromagnetic waves by an arbitrary configuration of parallel cylinders, a new formal solution that is different from the traditional ones to solve the problem of plane elastic waves scattering by cylindrical solid piles as barriers for environmental vibration isolation has been established. The first order of scattering is generated from the excitation of each pile by incident waves, and the second order is resulted from the excitation of each pile by the first order of scattering induced by remaining piles. The rest to an infinite can be executed in the same manner. Suppose that each order of scattering satisfies continuity boundary conditions at the surface of each pile, the undetermined scattering coefficients would be figured out ultimately. By introducing the normalized displacement amplitude and transmissibility indices, some properties of vibration isolation by single or multi-row of piles are analyzed. Influences of specific parameters such as scattering orders, separations between piles and pile rows, normalized frequencies, number of piles, etc. are investigated. Several instructive results are derived and recommended for designing piles as barriers for environmental vibration isolation.