Scattering of acoustic waves by movable lightweight elastic screens

Abstract This paper computes the insertion loss provided by movable lightweight elastic screens, placed over an elastic half-space, when subjected to spatially sinusoidal harmonic line pressure sources. A gap between the acoustic screen and the elastic floor is allowed. The problem is formulated in the frequency domain via the boundary element method (BEM). The Green's functions used in the BEM formulation permit the solution to be obtained without the discretization of the flat solid–ground interface. Thus, only the boundary of the elastic screen is modeled, which allows the BEM to be efficient even for high frequencies of excitation. The formulation of the problem takes into account the full interaction between the fluid (air) and the solid elastic interfaces. The validation of the algorithm uses a BEM model, which incorporates the Green's functions for a full space, requiring the full discretization of the ground. The model developed is then used to simulate the wave propagation in the vicinity of lightweight elastic screens with different dimensions and geometries. Both frequency and insertion loss results are computed over a grid of receivers. These results are also compared with those obtained with a rigid barrier and an infinite elastic panel.

[1]  António Tadeu,et al.  ACOUSTIC INSULATION OF SINGLE PANEL WALLS PROVIDED BY ANALYTICAL EXPRESSIONS VERSUS THE MASS LAW , 2002 .

[2]  Luiz C. Wrobel,et al.  A novel boundary integral formulation for three-dimensional analysis of thin acoustic barriers over an impedance plane , 1998 .

[3]  Y. Kawai,et al.  The application of integral equation methods to the calculation of sound attenuation by barriers , 1990 .

[4]  D. Duhamel.  EFFICIENT CALCULATION OF THE THREE-DIMENSIONAL SOUND PRESSURE FIELD AROUND A NOISE BARRIER , 1996 .

[5]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis: Part II (1986-1996) , 1997 .

[6]  Horace Lamb,et al.  On the propagation of tremors over the surface of an elastic solid , 1904, Proceedings of the Royal Society of London.

[7]  D. Duhamel,et al.  SOUND PROPAGATION OVER NOISE BARRIERS WITH ABSORBING GROUND , 1998 .

[8]  Robert A. Phinney,et al.  Theoretical calculation of the spectrum of first arrivals in layered elastic mediums , 1965 .

[9]  Luiz C. Wrobel,et al.  A DUAL BOUNDARY ELEMENT FORMULATION FOR SOUND PROPAGATION AROUND BARRIERS OVER AN IMPEDANCE PLANE , 1997 .

[10]  D. Beskos,et al.  Boundary Element Methods in Elastodynamics , 1988 .

[11]  T. Terai.  On calculation of sound fields around three dimensional objects by integral equation methods , 1980 .

[12]  K. R. Fyfe,et al.  A study of 2D and 3D barrier insertion loss using improved diffraction-based methods , 1998 .

[13]  Prasanta K. Banerjee,et al.  Time‐domain transient elastodynamic analysis of 3‐D solids by BEM , 1988 .

[14]  Simon N. Chandler-Wilde,et al.  INFLUENCE OF SHAPE AND ABSORBING SURFACE—A NUMERICAL STUDY OF RAILWAY NOISE BARRIERS , 1998 .

[15]  Paulo Santos,et al.  Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 2. SV-P wave propagation , 1999 .

[16]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis , 1987 .

[17]  Keiiti Aki,et al.  Discrete wave-number representation of seismic-source wave fields , 1977, Bulletin of the Seismological Society of America.

[18]  M. Bouchon.  Discrete wave number representation of elastic wave fields in three-space dimensions , 1979 .

[19]  António Tadeu,et al.  2.5D Green's Functions for Elastodynamic Problems in Layered Acoustic and Elastic Formations , 2001 .

[20]  Yiu W. Lam,et al.  Using Maekawa's chart to calculate finite length barrier insertion loss , 1994 .

[21]  E. Kausel,et al.  Green's Functions for Two-and-a-Half-Dimensional Elastodynamic Problems , 2000 .

[22]  P. Jean,et al.  THE IMPORTANCE OF SOURCE TYPE ON THE ASSESSMENT OF NOISE BARRIERS , 1999 .

[23]  A. J. B. Tadeua,et al.  Closed-form integration of singular terms for constant , linear and quadratic boundary elements . Part 2 . SVP wave propagation , 1999 .

[24]  Apostolos S. Papageorgiou,et al.  A Discrete Wavenumber Boundary Element Method for study of the 3‐D response 2‐D scatterers , 1998 .

[25]  Istvn L. Vr,et al.  Noise and Vibration Control Engineering , 2005 .

[26]  T M Barry,et al.  FHWA HIGHWAY TRAFFIC NOISE PREDICTION MODEL , 1978 .

[27]  Apostolos S. Papageorgiou,et al.  Discrete Wave‐Number Boundary‐Element Method for 3‐D Scattering Problems , 1993 .

[28]  Francisco J. Sánchez-Sesma,et al.  Three-dimensional scattering by two-dimensional topographies , 1994 .

[29]  António Tadeu,et al.  3D sound scattering by rigid barriers in the vicinity of tall buildings , 2001 .

[30]  F. S. Lamb,et al.  On the Propagation of Tremors over the Surface of an Elastic Solid , 1904 .