scholarly journals Radiation analysis of sound waves from semi-infinite coated pipe

2018 ◽  
Vol 18 (1) ◽  
pp. 92-111 ◽  
Author(s):  
Burhan Tiryakioglu ◽  
Ahmet Demir
Keyword(s):  
Fourier Transform ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Total Field ◽  
Hopf Equation ◽  
Waveguide Modes ◽  
Linear Algebraic Equations ◽  
Pipe Radius ◽  
Expansion Coefficients ◽  
The Fourier Transform

An analytical solution is presented for the problem of radiation of sound waves from a semi-infinite circular cylindrical coated pipe which is partially lined from inside. By stating the total field in duct region in terms of normal waveguide modes (Dini’s series) and using the Fourier transform technique elsewhere, we obtain a Wiener–Hopf equation whose solution involving three sets of infinitely many unknown expansion coefficients satisfying three systems of linear algebraic equations. This system is solved numerically and the influence of some parameters (pipe radius, impedances, extension, etc.) on the radiation phenomenon is displayed graphically.

scholarly journals Sound Transmission in a Duct with Sudden Area Expansion, Extended Inlet, and Lined Walls in Overlapping Region

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Ahmet Demir
Keyword(s):  
Fourier Transform ◽  
Numerical Solution ◽  
Sound Transmission ◽  
Algebraic Equations ◽  
Hopf Equation ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
The Fourier Transform ◽  
Area Expansion ◽  
Overlapping Region

The transmission of sound in a duct with sudden area expansion and extended inlet is investigated in the case where the walls of the duct lie in the finite overlapping region lined with acoustically absorbent materials. By using the series expansion in the overlap region and using the Fourier transform technique elsewhere we obtain a Wiener-Hopf equation whose solution involves a set of infinitely many unknown expansion coefficients satisfying a system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound transmission are studied.

scholarly journals Diffraction of sound waves by a lined cylindrical cavity

2020 ◽  
Vol 19 (1-2) ◽  
pp. 38-56
Author(s):  
Burhan Tiryakioglu
Keyword(s):  
Mode Matching ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Hopf Equation ◽  
Matching Method ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
The Fourier Transform ◽  
Sound Diffraction ◽  
Selection Of

In this paper, diffraction of sound waves through a lined cavity is analyzed rigorously. The inner–outer surfaces of the cavity and the base of the cavity are coated with three different absorbing linings. By using the Fourier transform technique in conjunction with the Mode-Matching method, the related boundary value problem is formulated as a Wiener–Hopf equation. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The graphical results are also presented which show that how efficiently the sound diffraction can be reduced by selection of problem parameters.

scholarly journals Analysis of Sound Waves with Semi Perforated Pipe

2019 ◽  
Vol 2 (3) ◽  
pp. 704-710
Author(s):  
Burhan Tiryakioglu
Keyword(s):  
Boundary Condition ◽  
Fourier Transform ◽  
Wave Equation ◽  
Pipe Wall ◽  
Far Field ◽  
Sound Waves ◽  
Hopf Equation ◽  
Hopf Method ◽  
The Fourier Transform ◽  
Perforated Pipe

The paper presents analytical results of radiation phenomena at the far field and solution of the wave equation with adequate boundary condition imposed by the pipe wall. An infinite pipe with perforated part is considered. The solution is obtained by using the Fourier transform technique in conjunction with the Wiener-Hopf Method. Applying the Fourier transform technique, the boundary value problem is described by Wiener Hopf equation and then solved analytically.

Diffraction by a set of three parallel impedance half-planes with the one amidst located in the opposite direction

2002 ◽  
Vol 80 (8) ◽  
pp. 893-909 ◽  
Author(s):  
G Çinar ◽  
A Büyükaksoy
Keyword(s):  
Fourier Transform ◽  
Opposite Direction ◽  
Infinite System ◽  
Plane Waves ◽  
Mode Matching ◽  
Algebraic Equations ◽  
Matching Method ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
The One

The problem of diffraction of plane waves by a set of three parallel half-planes with different surface impedances on upper and lower faces where the one in the middle is placed in the opposite direction, is solved by the mode-matching method where available, and by Fourier-transform technique elsewhere. The solution includes two independent Wiener–Hopf equations each involving an infinite number of expansion coefficients that satisfy an infinite system of linear algebraic equations. PACS No.: 41.20J

Sound Radiation from the Perforated End of a Lined Duct

2019 ◽  
Vol 105 (4) ◽  
pp. 591-599 ◽  
Author(s):  
Burhan Tiryakioglu
Keyword(s):  
Infinite System ◽  
Normal Modes ◽  
Mode Matching ◽  
Algebraic Equations ◽  
Matching Method ◽  
Linear Algebraic Equations ◽  
Matching Technique ◽  
Specific Impedance ◽  
Expansion Coefficients ◽  
The Fourier Transform

Radiation of sound wave through a lined duct with perforated end is analyzed rigorously. The problem considered is axisymmetric. By using the Fourier transform technique in conjunction with the Mode Matching method, the related boundary value problem is formulated as a Wiener-Hopf (W-H) equation. The Mode-Matching technique allows us to express the field component defined in the waveguide region in terms of normal modes. The solution involves a set of infinitely many expansion coefficients satisfying an infinite system of linear algebraic equations. The numerical solution of this system is obtained for different parameters of the problem such as the surface impedances, specific impedance of the perforated screen and their effects on the radiation phenomenon are shown graphically.

A Diagonally Dominant Solution for the Cylinder End Problem

1981 ◽  
Vol 48 (4) ◽  
pp. 876-880 ◽  
Author(s):  
T. D. Gerhardt ◽  
Shun Cheng
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Infinite Cylinder ◽  
Algebraic Equations ◽  
Precise Calculation ◽  
Linear Algebraic Equations ◽  
Present Solution ◽  
Diagonally Dominant ◽  
Expansion Coefficients

An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.

scholarly journals Numerical solution of a weakly singular integral equation by the method of orthogonal polynomials

2021 ◽  
pp. 98-103
Author(s):  
Sergei M. Sheshko
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Singular Integral ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
Analytical Expressions

A scheme is constructed for the numerical solution of a singular integral equation with a logarithmic kernel by the method of orthogonal polynomials. The proposed schemes for an approximate solution of the problem are based on the representation of the solution function in the form of a linear combination of the Chebyshev orthogonal polynomials and spectral relations that allows to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the Chebyshev polynomial basis are calculated by solving a system of linear algebraic equations. The results of numerical experiments show that on a grid of 20 –30 points, the error of the approximate solution reaches the minimum limit due to the error in representing real floating-point numbers.

scholarly journals Analysis of Directional Properties of Angular Horn Antenna

2021 ◽  
Vol 4 (3) ◽  
Author(s):  
Kateryna Andriivma Shyshkova
Keyword(s):  
Helmholtz Equation ◽  
Infinite System ◽  
Horn Antenna ◽  
Acoustic Properties ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Design Elements ◽  
Linear Algebraic Equations ◽  
Electroacoustic Transducer ◽  
Wide Range

In this paper, horn antennas are considered to belong to the class of aperture antennas which usually include a sound wave reflector and an electroacoustic transducer. For the variant of technical implementation of the electroacoustic transducer in the form of a corner antenna, the problem of sound emission by such an antenna is solved . taking into account the repeated reflection of emitted sound waves from the antenna design elements. The study of the acoustic properties of such an antenna was carried out taking into account a number of assumptions. 'what material, the thickness of the walls of the mouthpiece is infinitesimal. These conditions are supplemented by the known conditions of radiation at infinity. All the above assumptions make it possible to greatly simplify the solution of the problem of sound radiation by an angular horn antenna. To do this, the Helmholtz equation under boundary conditions was solved by the method of connected fields in multiconnected domains, corresponding to the physical model of the antenna. The radiation field of such an antenna is presented in the form of three partial regions, which in turn, according to the method of partial regions - in the form of Fourier series expansions, the coefficients of which are determined by solving differential equations describing piezoceramic transducer oscillations and wave processes. in acoustic environments in contact with it. The solution of the Helmholtz equation is reduced to the solution of an infinite system of linear algebraic equations taking into account the above assumptions, as well as the conditions of field continuity at the boundary of partial domains, we obtain an infinite system of linear algebraic equations. Based on the system, an approximate expression for the normalized radiation pattern is obtained. Studying the features of the directional properties of the angular antenna by direct analysis of the expression is not possible. Therefore, such a study was carried out on the basis of calculated directivity diagrams obtained using a computer for a wide range of wave sizes and geometrical characteristics of the angular antenna. cylindrical electroacoustic transducers. In all calculations, a uniform distribution of the oscillating velocity on the surface of the emitter was chosen Analyzing the obtained data, there is a pronounced dependence of the shape of the pattern on the magnitude of the wave size of the speaker. This is manifested in the fact that the main petal splits into two or even three petals, as well as in increasing the overall sharpness of the pattern.  

Reply by authors to discussion by Gudmundur Gudmundsson

Geophysics ◽  
1971 ◽  
Vol 36 (3) ◽  
pp. 617-618
Author(s):  
Allan Spector ◽  
Fraser S. Grant
Keyword(s):  
Fourier Transform ◽  
Mathematical Expression ◽  
Fundamental Difference ◽  
Total Field ◽  
The Fourier Transform

The authors appreciate the interest shown by Gudmundsson in their paper. They wish also to correct his observation that there is a fundamental difference between the mathematical expression for the Fourier transform of the total field anomaly due to a prism, given by Bhattacharyya (1966), and the basis of that given in their paper.

scholarly journals The interaction of a contact discontinuity with sound waves according to the linearised Navier-Stokes equations

1970 ◽  
Vol 17 (1) ◽  
pp. 37-46
Author(s):  
W. M. Anderson
Keyword(s):  
Fourier Transform ◽  
Contact Surface ◽  
Stokes Equations ◽  
Asymptotic Series ◽  
Density Perturbation ◽  
Navier Stokes ◽  
Sound Waves ◽  
Navier Stokes Equations ◽  
Initial Discontinuity ◽  
The Fourier Transform

AbstractThe resolution of a small initial discontinuity in a gas is examined using the linearised Navier-Stokes equations. The smoothing of the resultant contact surface and sound waves due to dissipation results in small flows which interact. The problem is solved for arbitrary Prandtl number by using a Fourier transform in space and a Laplace transform in time. The Fourier transform is inverted exactly and the density perturbation is found as two asymptotic series valid for small dissipation near the contact surface and the sound waves respectively. The modifications to the structures of the contact surface and the sound waves are exhibited.

Sign in / Sign up

Export Citation Format

Share Document