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Meccanica

, Volume 9, Issue 2, pp 70–74 | Cite as

Scattering of implusive sound waves by a rigid cylinder

  • Roberto Forghieri
  • Giorgio Papa
Article

Summary

Analytic time solutions for the scattering of impulsive waves (the time-space Green function) by a rigid circular cylinder in an annular domain are obtained through a finite integral transform of the spatial variable.

By a similar generalized procedure the scattering of impulsive waves by a rigid cylinder in an infinite medium is described in order to obtain the Green function of the reduced wave equation in terms of a series of “propagation modes”.

Keywords

Mechanical Engineer Civil Engineer Spatial Variable Wave Equation Generalize Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

r1,m

Radius of the rigid circular cylinder and inner radius of the annular domain

r2,m

outer radius of the annular domain

r0,m

distance of the impulsive source from the centre of the cylinder

c, m sec−1

propagation velocity of perturbation

V(r), W(r)

kernels

r, m

spatial variable

θ, rad

angular variable

t, sec

time variable

s, sec−1

Laplace transformation variable

v, n

Fourier transformation variables

p, q

integral transformation variables

Sommario

In questo articolo si presentano alcuni metodi di soluzione analitica di problemi di diffrazione di onde impulsive in un dominio anulare. Le soluzioni sono ottenute con l'impiego di una trasformata integrale finita della variabile spaziale.

Attraverso un procedimento analogo generalizzato viene descritta la diffrazione di onde impulsive causate da un cilindro circolare rigido in un mezzo infinito.

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References

  1. [1]
    F. G. Friedlander,Diffraction of Pulses by a Circular Cylinder Comm. on Pure and Appl. Math., Vol. 7, pp. 705–732, 1954.Google Scholar
  2. [2]
    F. G.Friedlander,Sound Pulses, Cambridge University Press, 1958.Google Scholar
  3. [3]
    J. Martinek andH. P. Thielman,On Green's functions for the reduced wave equation in a circular annular domain with Dirichlet, Neumann and radiation type boundary conditions, Appl. Sci. Re., Vol. 16, pp. 5–12, 1966.Google Scholar
  4. [4]
    J. Weil, Tadepalli, S. Murty andDesirajn B. Rao,Zeroes of J n (λ)Y n (ηλ)−J n (ηλ)Y n (λ) andJ n '(λ)Y n '(ηλ)−−J n '(ηλ)Y n '(λ), Math. Comp., Vol. 21, pp. 722–727, 1967.Google Scholar

Copyright information

© Tamburini Editore 1974

Authors and Affiliations

  • Roberto Forghieri
    • 1
  • Giorgio Papa
    • 1
  1. 1.Centro di CalcoloCNENBologna

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