NON-PARABOLIC MARCHING ALGORITHM FOR SOUND FIELD CALCULATION IN THE OCEAN WAVEGUIDE

1996 ◽  
Vol 04 (04) ◽  
pp. 399-423 ◽  
Author(s):  
A. VORONOVICH
Keyword(s):  
Sound Propagation ◽  
A Priori ◽  
Numerical Algorithms ◽  
Sound Field ◽  
Computer Code ◽  
Couple Mode ◽  
Field Calculation ◽  
Piecewise Constant ◽  
S Matrix ◽  
Piecewise Constant Approximation

An algorithm is presented for calculating sound field in the inhomogeneous ocean waveguide. It does not involve parabolic approximation and can be considered as principally exact (at least for 2D inhomogeneities of the sound speed field). On the other hand, it is “marching” and can be easily implemented as a computer code (note, that marching in this case proceeds in “backward” direction, i.e. towards the source). Those features of the code are similar to couple mode algorithm (COUPLE) developed originally by R. Evans. The principal difference is that suggested code does not assume piecewise constant approximation of the waveguide properties with respect to horizontal coordinates. As a result, the horizontal steps of marching can be increased significantly. The estimate of the efficiency of the approach as compared to stepwise couple modes method is given. The results of the code testing with the help of benchmark problem as well as calculation of sound propagation through a strong inhomogeneity formed by the sub-arctic front are presented. The present version of the code can be used to calculate entries of scattering matrix (S-matrix) for the ocean waveguide as well as travel times of different modes (derivatives of phases of corresponding entries with respect to frequency). A priori restrictions on S-matrix (reciprocity and energy conservation) are also given, and some objective quantitative criterion of the accuracy of the numerical algorithms formulated in terms of S-matrix is suggested.

scholarly journals Improving the Performance of Mode-Based Sound Propagation Models by Using Perturbation Formulae for Eigenvalues and Eigenfunctions

2021 ◽  
Vol 9 (9) ◽  
pp. 934
Author(s):  
Alena Zakharenko ◽  
Mikhail Trofimov ◽  
Pavel Petrov
Keyword(s):  
Sound Propagation ◽  
Underwater Acoustics ◽  
Computational Cost ◽  
Normal Modes ◽  
Sound Field ◽  
Field Calculation ◽  
Combined Model ◽  
Eigenvalues And Eigenfunctions ◽  
Propagation Models ◽  
Area Of Interest

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.

scholarly journals Numerical and Experimental Studies on Inclined Incidence Parametric Sound Propagation

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Haisen Li ◽  
Jingxin Ma ◽  
Jianjun Zhu ◽  
Baowei Chen
Keyword(s):  
Sound Propagation ◽  
Experimental Studies ◽  
Sound Field ◽  
Source Model ◽  
Calculation Model ◽  
Theoretical Research ◽  
Field Calculation ◽  
Sound Beam ◽  
Sound Fields ◽  
Kzk Equation

The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation has been widely used in the simulation and calculation of nonlinear sound fields. However, the accuracy of KZK equation reduced due to the deflection of the direction of the sound beam when the sound beam is inclined incidence. In this paper, an equivalent sound source model is proposed to make the calculation direction of KZK calculation model consistent with the sound propagation direction after acoustic refraction, so as to improve the accuracy of sound field calculation under the inclined incident conditions. The theoretical research and pool experiment verify the feasibility and effectiveness of the proposed method.

High Amplitude Sound Propagation at Low Frequencies in a Flow Duct Lined With Resonators: A Time Domain Solution

1988 ◽  
Vol 110 (4) ◽  
pp. 545-551 ◽  
Author(s):  
A. Cummings ◽  
I.-J. Chang
Keyword(s):  
Time Domain ◽  
Internal Combustion Engines ◽  
Sound Propagation ◽  
Sound Field ◽  
High Amplitude ◽  
Combustion Engines ◽  
Low Frequencies ◽  
The Time Domain ◽  
Flow Duct ◽  
Good Agreement

A quasi one-dimensional analysis of sound transmission in a flow duct lined with an array of nonlinear resonators is described. The solution to the equations describing the sound field and the hydrodynamic flow in the neighborhood of the resonator orifices is performed numerically in the time domain, with the object of properly accounting for the nonlinear interaction between the acoustic field and the resonators. Experimental data are compared to numerical computations in the time domain and generally very good agreement is noted. The method described here may readily be extended for use in the design of exhaust mufflers for internal combustion engines.

scholarly journals Sound diffraction on an elastic spheroidal shell

2021 ◽  
Vol 3 (397) ◽  
pp. 97-114
Author(s):  
A. Kleschev ◽  
Keyword(s):  
Group Velocity ◽  
Planar Waveguide ◽  
Sound Propagation ◽  
Spectral Characteristics ◽  
Sound Field ◽  
Signal Propagation ◽  
Elastic Bottom ◽  
Harmonic Signals ◽  
Scattered Fields ◽  
Sound Diffraction

Object and purpose of research. This paper obtains solutions and performs estimations of characteristics of sound reflection and scattering by ideal and elastic bodies of various shapes (analytical and non-analytical) near media interface, or underwater sonic channel, or in a planar waveguide with a solid elastic bottom. Materials and methods. The harmonic signals are investigated with the method of normal waves based on the phase velocity of signal propagation, and impulse signals related to the energy transfer are studied using the method of real and imaginary sources and scatterers based on the group velocity of propagation. Main results. The scattered sound field is calculated for ideal spheroids (elongated and compressed) at fluid – ideal medium interface. The spectrum of a scattered impulse signal is calculated for a body placed in a sonic channel. First reflected impulses are found for an ideal spheroid in a planar waveguide with anisotropic bottom. Conclusion. In the studies of diffraction characteristics of bodies at media interfaces it was found that the main contribution to scattered field is given by interference of scattered fields rather than interaction of scatterers (real or imaginary). It is shown that at long distances the spectral characteristics of the channel itself have a prevalent role. When impulse sound signals in the planar waveguide are used, it is necessary to apply the method of real and imaginary sources and scatterers based on the group velocity of sound propagation.

ReLU Networks Are Universal Approximators via Piecewise Linear or Constant Functions

2020 ◽  
Vol 32 (11) ◽  
pp. 2249-2278
Author(s):  
Changcun Huang
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Piecewise Linear Approximation ◽  
Piecewise Constant ◽  
Deep Layers ◽  
Univariate Function ◽  
Arbitrary Precision ◽  
Piecewise Constant Approximation ◽  
Neural Unit ◽  
Universal Approximators

This letter proves that a ReLU network can approximate any continuous function with arbitrary precision by means of piecewise linear or constant approximations. For univariate function [Formula: see text], we use the composite of ReLUs to produce a line segment; all of the subnetworks of line segments comprise a ReLU network, which is a piecewise linear approximation to [Formula: see text]. For multivariate function [Formula: see text], ReLU networks are constructed to approximate a piecewise linear function derived from triangulation methods approximating [Formula: see text]. A neural unit called TRLU is designed by a ReLU network; the piecewise constant approximation, such as Haar wavelets, is implemented by rectifying the linear output of a ReLU network via TRLUs. New interpretations of deep layers, as well as some other results, are also presented.

Comparison of Sound Propagation Characteristic between Deep and Shallow Water

2014 ◽  
Vol 577 ◽  
pp. 1198-1201
Author(s):  
Zhang Liang ◽  
Chun Xia Meng ◽  
Hai Tao Xiao
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Sound Speed ◽  
Sound Propagation ◽  
Spherical Wave ◽  
Sound Field ◽  
Propagation Loss ◽  
Speed Profile ◽  
Sound Speed Profile ◽  
Propagation Law

The physical characteristics are compared between shallow and deep water, in physics and acoustics, respectively. There is a specific sound speed profile in deep water, which is different from which in shallow water, resulting in different sound propagation law between them. In this paper, the sound field distributions are simulated under respective typical sound speed profile. The color figures of sound intensity are obtained, in which the horizontal ordinate is distance, and the vertical ordinate is depth. Then we can get some important characteristics of sound propagation. The results show that the seabed boundary is an important influence on sound propagation in shallow water, and sound propagation loss in deep water convergent zone is visibly less than which in spherical wave spreading. We can realize the remote probing using the acoustic phenomenon.

Synthetic Sound Source Generation for Acoustical Measurements in Turbomachines

2013 ◽  
Author(s):  
Michael Bartelt ◽  
Juan D. Laguna ◽  
Joerg R. Seume
Keyword(s):  
Wind Tunnel ◽  
Sound Source ◽  
Sound Propagation ◽  
Microphone Array ◽  
Sound Field ◽  
Acoustic Mode ◽  
Acoustic Excitation ◽  
Noise Emission ◽  
Noise Sources ◽  
Sound Fields

One of the greatest challenges in modern aircraft propulsion design is the reduction of the engine noise emission in order to develop quieter aircrafts. In the course of a current research project, the sound transport in low pressure turbines is investigated. For the corresponding experimental measurements, a specific acoustic excitation system is developed which can be implemented into the inlet of a turbine test rig and into an aeroacoustic wind tunnel. This allows for an acoustic mode generation and a synthesis of various sound source patterns to simulate typical turbomachinery noise sources such as rotor-stator interaction, etc. The paper presents the acoustical and technical design methodology in detail and addresses the experimental options of the system. Particular attention is paid to the design and the numerical optimization of the acoustic excitation units. To validate the sound generator during operation, measurements are performed in an aeroacoustic wind tunnel. For this purpose, an in-duct microphone array with a specific beamforming algorithm for hard-walled ducts is developed and applied to identify the source locations. The synthetically excited sound fields and the propagating acoustic modes are measured and analyzed by means of modal decomposition techniques. The measurement principles and the results are discussed in detail and it is shown that the intended sound source is produced and the intended sound field is excited. This paper shall contribute to help guide the development of excitation systems for aeroacoustic experiments to better understanding the physics of sound propagation within turbomachines.

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