Scattering of a Plane Acoustic Wave by a Spherical Elastic Shell Near a Free Surface

1995 ◽  
Author(s):  
H. Huang ◽  
G. C. Gaunaurd
Keyword(s):  
Free Surface ◽  
Separation Of Variables ◽  
Mathematical Problem ◽  
Elastic Shell ◽  
Plane Waves ◽  
Spherical Wave ◽  
Acoustic Scattering ◽  
Scattered Wave ◽  
Image Method ◽  
Spherical Elastic Shell

Abstract The acoustic scattering by a submerged spherical elastic shell near a free surface, and insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion using the classical separation of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell, the mathematical problem is formulated using the image method. The scattering wave fields are expanded in terms of the classical modal series of spherical wave functions utilizing the translational addition theorem. Quite similar to the problem of scattering by multiple spheres, the numerical computation of the scattered wave pressure involves the solution of an ill-conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and the proximity of the spherical elastic shell to the free surface. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method and Twersky’s method of successive iteration double checking each other. Backscattered echoes from the spherical elastic shell are extensively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerged elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibration.

ACOUSTIC SCATTERING FROM AN ELASTIC SPHERICAL SHELL IN AN OCEANIC WAVEGUIDE WITH A PENETRABLE BOTTOM

2013 ◽  
Vol 21 (03) ◽  
pp. 1350009 ◽  
Author(s):  
NATALIE S. GRIGORIEVA ◽  
GREGORY M. FRIDMAN
Keyword(s):  
Normal Mode ◽  
Critical Frequency ◽  
Transmission Loss ◽  
Elastic Shell ◽  
Acoustic Scattering ◽  
Oceanic Waveguide ◽  
Homogeneous Fluid ◽  
Scattering Coefficients ◽  
Spherical Elastic Shell ◽  
Probability Integral

The paper describes the theory and implementation issues of modeling of the acoustic field scattered by an air-filled spherical elastic shell immersed in a shallow-water waveguide over a homogeneous, fluid half-space. The normal mode evaluation is applied to the source contribution and to the scattering coefficients. The arising branch cut integrals are simplified and expressed via the probability integral. Two cases are analyzed: when a source frequency differs from the critical frequency of a normal mode and when they coincide. The formalism is applied to evaluate the effect of coupling between propagation and scattering on transmission loss.

ACOUSTIC SCATTERING BY AN ELASTIC SPHERICAL SHELL NEAR THE SEABED

2012 ◽  
Vol 20 (03) ◽  
pp. 1250006 ◽  
Author(s):  
JEAN-PIERRE SESSAREGO ◽  
PAUL CRISTINI ◽  
NATALIE S. GRIGORIEVA ◽  
GREGORY M. FRIDMAN
Keyword(s):  
Spherical Shell ◽  
Elastic Shell ◽  
Acoustic Scattering ◽  
Compressional Wave ◽  
Wide Frequency Range ◽  
Strong Interactions ◽  
Frequency Range ◽  
Symmetric Wave ◽  
Spherical Elastic Shell ◽  
Single Scatter

The paper describes the theory and implementation issues of modeling of the backscattered field from a thin air-filled spherical elastic shell immersed in water close to the seabed or to the air/water interface. Computational results obtained for the full multiple scattering solution are compared with the model utilizing the single-scatter approximation in a wide-frequency range 0 < k0a ≤ 55. In this frequency range for a thin air-filled spherical shell the main elastic contribution to scattering is due to the lowest-order compressional wave which is the generalization of the Lamb symmetric wave of a flat plate and due to the subsonic mode of the first antisymmetric Lamb wave. Strong resonance peaks produced by these waves in the backscattered form functions have been identified in numerical modeling. It has been shown that when the object is close to the interface in addition to geometrical reflections between the shell and the interface, strong interactions due to these resonances can be observed.

Time-frequency analysis of the bistatic acoustic scattering from a spherical elastic shell

2012 ◽  
Vol 131 (1) ◽  
pp. 164-173 ◽  
Author(s):  
Shaun D. Anderson ◽  
Karim G. Sabra ◽  
Manell E. Zakharia ◽  
Jean-Pierre Sessarego
Keyword(s):  
Frequency Analysis ◽  
Elastic Shell ◽  
Acoustic Scattering ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Spherical Elastic Shell

scholarly journals Neoclassical Solution of Transient Interaction of Plane Acoustic Waves with a Spherical Elastic Shell

1996 ◽  
Vol 3 (2) ◽  
pp. 85-98 ◽  
Author(s):  
Hanson Huang ◽  
Hans U. Mair
Keyword(s):  
Laplace Transform ◽  
Acoustic Waves ◽  
Separation Of Variables ◽  
Elastic Shell ◽  
Time Derivative ◽  
Time History ◽  
Inverse Laplace Transform ◽  
Transient Interaction ◽  
Time Histories ◽  
Spherical Elastic Shell

A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.

scholarly journals Localization of Scattering Objects Using Neural Networks

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 11
Author(s):  
Domonkos Haffner ◽  
Ferenc Izsák
Keyword(s):  
Neural Networks ◽  
Plane Waves ◽  
Measurement Data ◽  
Scattered Wave ◽  
Training Data ◽  
Data Set ◽  
Main Compound ◽  
Incident Plane ◽  
The Neural Networks ◽  
Simulation Package

The localization of multiple scattering objects is performed while using scattered waves. An up-to-date approach: neural networks are used to estimate the corresponding locations. In the scattering phenomenon under investigation, we assume known incident plane waves, fully reflecting balls with known diameters and measurement data of the scattered wave on one fixed segment. The training data are constructed while using the simulation package μ-diff in Matlab. The structure of the neural networks, which are widely used for similar purposes, is further developed. A complex locally connected layer is the main compound of the proposed setup. With this and an appropriate preprocessing of the training data set, the number of parameters can be kept at a relatively low level. As a result, using a relatively large training data set, the unknown locations of the objects can be estimated effectively.

scholarly journals A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

2021 ◽  
Vol 11 (6) ◽  
pp. 2722
Author(s):  
Zhiwen Qian ◽  
Dejiang Shang ◽  
Yuan Hu ◽  
Xinyang Xu ◽  
Haihan Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Sound Field ◽  
Efficient Computation ◽  
Image Source ◽  
Source Method ◽  
Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

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