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

Abstract 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.

[1]  Francisco J. Sánchez-Sesma,et al.  Piles as Barriers for Elastic Waves , 1983 .

[2]  V. Twersky,et al.  Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders , 1952 .

[3]  Jian-Hua Wang,et al.  Numerical analysis of isolation of the vibration due to moving loads using pile rows , 2009 .

[4]  John William Strutt,et al.  Scientific Papers: On the Passage of Waves through Apertures in Plane Screens, and Allied Problems , 2009 .

[5]  Lord Rayleigh F.R.S..  XXXVII. On the passage of waves through apertures in Plane screens, and allied problems , 1897 .

[6]  Richard D. Woods,et al.  HOLOGRAPHY--A NEW TOOL FOR SOIL DYNAMICS , 1974 .

[7]  Changjie Xu,et al.  Amplitude reduction of elastic waves by a row of piles in poroelastic soil , 2009 .

[8]  Francisco J. Sánchez-Sesma,et al.  Foundation Isolation from Vibrations Using Piles as Barriers , 1988 .

[9]  Yih-Hsing Pao,et al.  Diffraction of elastic waves and dynamic stress concentrations , 1973 .

[10]  G. Gao,et al.  Three-dimensional analysis of rows of piles as passive barriers for ground vibration isolation , 2006 .

[11]  Dimitri E. Beskos,et al.  Vibration isolation using open or filled trenches , 1986 .

[12]  V. Twersky,et al.  Multiple Scattering of Radiation by an Arbitrary Planar Configuration of Parallel Cylinders and by Two Parallel Cylinders , 1952 .

[13]  Demosthenes Polyzos,et al.  Vibration isolation by a row of piles using a 3‐D frequency domain BEM , 1999 .

[14]  S. L. Cheng.  Multiple Scattering of Elastic Waves by Parallel Cylinders , 1969 .

[15]  Yuanqiang Cai,et al.  Vertical amplitude reduction of Rayleigh waves by a row of piles in a poroelastic half‐space , 2009 .

[16]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[17]  A. Robert,et al.  James E. Vance Jr. The merchant's world : the geography of wholesaling. Englewood Cliffs (NJ), Prentice Hall, Foundations of Economic Geography Series, 1970 , 1972 .

[18]  J. Lysmer,et al.  Shear Waves in Plane Infinite Structures , 1972 .

[19]  Changjie Xu,et al.  Screening of plane S waves by an array of rigid piles in poroelastic soil , 2008 .

[20]  Zheng-Yi Feng,et al.  Three-dimensional analysis of the screening effectiveness of hollow pile barriers for foundation-induced vertical vibration , 2008 .

[21]  Demosthenes Polyzos,et al.  Modelling of pile wave barriers by effective trenches and their screening effectiveness , 1999 .

[22]  T. M. Al-Hussaini,et al.  DESIGN OF WAVE BARRIERS FOR REDUCTION OF HORIZONTAL GROUND VIBRATION , 1991 .

[23]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[24]  F. E. Richart,et al.  Vibrations of soils and foundations , 1970 .