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Influence of the position of the opening and its shape on the properties of a Helmholtz resonator

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Abstract

The method of matched asymptotic expansions is used to influence the choice of the position of the opening and its shape on the properties of a Helmholtz acoustic resonator. It is shown that these parameters influence the imaginary part of the pole of the analytic continuation of the Green's function of the Helmholtz resonator, which, in its turn, has a strong influence on the behavior of the solutions of the corresponding scattering and radiation problems.

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References

  1. O. M. Rayleigh,Proc. R. Soc. London. Ser. A,92, 265 (1916).

    Google Scholar 

  2. J. W. Miles,J. Acoust. Soc. Am.,50, 892 (1971).

    Google Scholar 

  3. A. A. Arsen'ev,Zh. Vychisl. Mat. Mat. Fiz.,12, 112 (1972).

    Google Scholar 

  4. J. T. Beale,Commun. Pure Appl. Math.,26, 549 (1973).

    Google Scholar 

  5. S. V. Petras,Funktsional Analiz i Ego Prilozhen.,9, 89 (1975).

    Google Scholar 

  6. R. R. Gadyl'shin,Dokl. Akad. Nauk SSSR,310, 1094 (1990).

    Google Scholar 

  7. R. R. Gadyl'shin,Algebra i Analiz,4 88 (1992).

    Google Scholar 

  8. D. L. Colton and R. Kress,Integral Equation Methods in Scattering Theory, Wiley, New York (1983).

    Google Scholar 

  9. G. Pólya and G. Szegö,Isoperimetric Inequalities in Mathematical Physics, Princeton (1951).

  10. H. S. Landkof,Foundations of Modern Potential Theory, Springer, Berlin (1972).

    Google Scholar 

  11. M. D. Van Dyke,Perturbation Methods in Fluid Mechanics, New York (1964).

  12. A. M. Il'in,Matching of Asymptotic Expansions of the Solutions of Boundary-Value Problems [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  13. V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii,Izv. Akad. Nauk SSSR, Ser. Mat.,48, 347 (1984).

    Google Scholar 

  14. R. R. Gadyl'shin,Dif. Uravneniya,22, 640 (1986).

    Google Scholar 

  15. B. S. Pavlov and M. D. Faddeev,Zap. Nauchn. Sem. Leningrad Branch, V. A. Steklov Mathematics Institute,126, 159 (1983).

    Google Scholar 

  16. I. Yu. Popov,Mat. Sb.,181, 1366 (1990).

    Google Scholar 

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Authors
  1. R. R. Gadyl'shin
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Institute of Mathematics with Computational Center of the Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 1, pp. 107–118, October, 1992.

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Gadyl'shin, R.R. Influence of the position of the opening and its shape on the properties of a Helmholtz resonator. Theor Math Phys 93, 1151–1159 (1992). https://doi.org/10.1007/BF01016473

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  • DOI: https://doi.org/10.1007/BF01016473

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