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Scattering of implusive sound waves by a rigid cylinder

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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.

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”.

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Abbreviations

r 1,m :

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

r 2,m :

outer radius of the annular domain

r 0,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

References

  1. F. G. Friedlander,Diffraction of Pulses by a Circular Cylinder Comm. on Pure and Appl. Math., Vol. 7, pp. 705–732, 1954.

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  2. F. G.Friedlander,Sound Pulses, Cambridge University Press, 1958.

  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.

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  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.

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Authors and Affiliations

  1. Centro di Calcolo, CNEN, Bologna

    Roberto Forghieri & Giorgio Papa

Authors
  1. Roberto Forghieri
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  2. Giorgio Papa
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Additional information

This work was supported by C.N.R., Committee for Mathematical Sciences.

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Forghieri, R., Papa, G. Scattering of implusive sound waves by a rigid cylinder. Meccanica 9, 70–74 (1974). https://doi.org/10.1007/BF02209508

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  • DOI: https://doi.org/10.1007/BF02209508

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