An Exact Analysis of the Transient Interaction of Acoustic Plane Waves With a Cylindrical Elastic Shell

1970 ◽  
Vol 37 (4) ◽  
pp. 1091-1099 ◽  
Author(s):  
H. Huang
Keyword(s):  
Integral Equations ◽  
Acoustic Waves ◽  
Linear Problem ◽  
Elastic Shell ◽  
Plane Waves ◽  
Integration Scheme ◽  
Elastic Cylindrical Shell ◽  
Governing System ◽  
Roundoff Errors ◽  
Transient Interaction

The governing system of differential equations for the linear problem of the transient interaction of plane acoustic waves and a submerged elastic cylindrical shell is transformed into a system of Volterra integral equations of the second kind. The integral equations are solved by a step-by-step integration scheme and numerical results to the problem are obtained exactly within the limit of series solution imposed by the Gibb’s phenomenon and within the limit of numerical truncation and roundoff errors. Detailed features of the transient response of the shell were revealed.

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.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

Calculation of Acoustic Efficiency of Exhaust Silencers for Automotive Internal Combustion Engines

2021 ◽  
pp. 41-47
Author(s):  
Vladimir Tupov ◽  
O. Matasova
Keyword(s):  
Acoustic Waves ◽  
Internal Combustion Engines ◽  
Combustion Engine ◽  
Control Point ◽  
Plane Waves ◽  
Exhaust System ◽  
Internal Combustion ◽  
Combustion Engines ◽  
Exhaust Noise ◽  
Insertion Losses

Insertion losses as the main characteristic that mathematically describes the acoustic efficiency of a noise silencer has been considered. This characteristic shows the reduction of noise generated by its source, in particular by the internal combustion engine’s exhaust system, at the control point as a silencer use result. Has been presented a mathematical description of the insertion losses, and have been considered parameters necessary for calculating this characteristic. Has been demonstrated the analytical dependence of impedance for the sound emission by the exhaust system’s end hole from the coefficient of acoustic waves reflection by this hole. The performed analysis of the widely used formulas for calculating the coefficient of sound reflection by the end hole has showed their insufficient accuracy for project designs performing. Have been proposed calculation dependences providing high accuracy for calculations of the reflection coefficient modulus, and the attached length of the channel end hole without a flange in the entire range of the existence of plane waves in it. It has been shown that the end correction of this hole at ka = 0 is 0.6127, and not 0.6133, as it was mistakenly believed until now in world acoustics. Has been proposed a method for calculation the exhaust noise source internal impedance. This method more accurately, in comparison with the already known ones, describes the acoustic processes in the internal combustion engine’s exhaust manifold, thanks to increases the accuracy of calculation the silencer acoustic efficiency, that allows develop the silencer at the early stages of the design of an automotive internal combustion engine.

Composites with invisible inclusions: Eigenvalues of ℝ-linear problem

2016 ◽  
Vol 27 (5) ◽  
pp. 796-806
Author(s):  
V. V. MITYUSHEV
Keyword(s):  
Asymptotic Formula ◽  
Integral Equations ◽  
Linear Problem ◽  
Nodal Domains

A new eigenvalue ℝ-linear problem arisen in the theory of metamaterials and neutral inclusions is reduced to integral equations. The problem is constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of inclusions tend to zero. The nodal domains conjecture related to univalent eigenfunctions is posed. Demonstration of the conjecture allows to justify that a set of inclusions can be made neutral by surrounding it with an appropriate coating.

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