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Numerical Method for Hetero-Cavities Natural Frequencies’ Determination


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DOI: https://doi.org/10.15866/ireme.v10i3.8913

Abstract


Noise elimination and sound intensity reduction are significantly one of the most important scientific topics. Thanks to the researches on natural frequencies, this subject has started to find a satisfactory answer. Nevertheless, the natural frequencies calculation is still complicated. Assuming the paraxial approximation of the Helmholtz equation, a simple method for natural frequency determination is developed. Our method is available for any number of non-symmetrical, non-periodical hetero-cavities. It can be applied on a multi-cavities system with varying length and cross-area. To illustrate the feasibility of the proposed method, cases of simple tube, Helmholtz resonator and multi-cavities systems have been examined. The proposed method is found to be useful for any number of cavities arranged in any random way making it more realistic, simple, and valid for cavities analysis and design.
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Keywords


Natural Frequency; Helmholtz Resonator; Multi-Cavities; Allowed Band

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References


Tang PK, Sirignano WA. Theory of generalized Helmholtz resonator. J. Sound Vib. 26, 247-62,1973.
http://dx.doi.org/10.1016/s0022-460x(73)80234-2

Panton RL, Miller JM. Resonant frequencies of cylindrical Helmholtz resonators. J Acoustic SosAm 57,1533-5,1975.

Alster M. Improved calculation of resonant frequencies of Helmholtz resonators. J Sound Vib.24:63-85,1972.
http://dx.doi.org/10.1016/0022-460x(72)90123-x

Munjal ML. Acoustics of ducts and mufflers with application to exhaust and ventilation system design New York: Wiley; 1987.

X. Li and G. Raman, Numerical methods for nonlinear acoustic resonators, Computational Methods in Nonlinear Acoustics. Current Trends, 2011: 21-31.

N. Chanpong, Z. Mohammad, H. Wei, S. Watkins, X. Wang, A study of tyre cavity resonance and its mitgation using modal analysis method, Inter-noise 2014, Melbourne Australia, November 16-19.

A. M. Akhtyamov and E.I. Satyev, Determination of the position and volume of a cavity in an elastic rod from its two vibration eigenfrequencies. Russian Journal of Nondestructive Testing 48(5) 2012.
http://dx.doi.org/10.1134/s1061830912050026

M. Petyt, G.H. Koopmann , R.J. Pinnington, The acoustic modes of a rectangular cavity containing a rigid, incomplete partition. Journal of Sound and Vibration, Volume 53, Issue 1, Page 71¬82, 1977.
http://dx.doi.org/10.1016/0022-460x(77)90095-5

Daniel A. Russell, Basketballs as spherical acoustic cavities. Am. J. Phys. 78, 6, 2010.
http://dx.doi.org/10.1119/1.3290176

C. G. Provatidis, Eigenanalysis of two-dimensional acoustic cavities using transfinite interpolation. Journal of Algorithms & Computational Technology, 3, 4, 2009.
http://dx.doi.org/10.1260/174830109789621383

D. Rockwell and E. Naudascher Review—Self¬Sustaining Oscillations of Flow Past Cavities. J. Fluids Eng 100 (2), 152¬165 1978 .
http://dx.doi.org/10.1115/1.3448624

J. M. Heinz and K. N. Stevens, On the Properties of Voiceless Fricative Consonants. J. Acoust. Soc. Am. 33, 589 1961.
http://dx.doi.org/10.1121/1.1908734

W. P. Baker, G. A. Kriegsmann and E. L. Reiss, Acoustic scattering by baffled cavity-backed membranes, J. Acoust. Soc. Am. 83, 423 (1988).
http://dx.doi.org/10.1121/1.396543

Alvarez, J. O., Kerschen, E. J., &Tumin, A. A theoretical model for cavity acoustic resonances in subsonic flow. Aeroacoustics Conference. 1, 532-543, 2004.
http://dx.doi.org/10.2514/6.2004-2845

Tang SK. On Helmholtz resonators with tapered necks. J. Sound Vib. 279, 1085-96, 2005.
http://dx.doi.org/10.1016/j.jsv.2003.11.032

Griffin S, Lane SA, Huybrechts S. Coupled Helmholtz resonators for acoustic attenuation. J. VibAcoust123,7-11,2001.
http://dx.doi.org/10.1115/1.1320812

Wan DM, Soedel DT, Two degree of freedom Helmholtz resonator analysis. SAE 01, 0387,2004.
http://dx.doi.org/10.4271/2004-01-0387

M. B. Xu, A. Selamet and H. Kim, Dual Helmholtz resonator, Applied Acoustics 71, 822-829, 2010.
http://dx.doi.org/10.1016/j.apacoust.2010.04.007

Cora et Al. Acoustic instabilities control using Helmholtz resonators. Applied Acoustics, 77, 1–10, 2014.
http://dx.doi.org/10.1016/j.apacoust.2013.09.013

W. M. Lee. Acoustic eigenproblems of elliptical cylindrical cavities with multiple elliptical cylinders by using the collocation multipole method. International Journal of Mechanical Sciences 78, 203–214, 2014.
http://dx.doi.org/10.1016/j.ijmecsci.2013.11.013

D. Li and L. Cheng, Acoustically coupled model of an enclosure and a Helmholtz resonator array, J Sound Vib305, 272–288, 2007.
http://dx.doi.org/10.1016/j.jsv.2007.04.009

F. Maiz, A. Hfaiedh, N. Yacoubi, A simple method for the determination of superlattice, J. Appl. Phys. 83867-869(1998).
http://dx.doi.org/10.1063/1.366769

F. Maiz, Superlattice band structure: New and simple energy quantification condition, Physica B 450, 67–70, 2014.
http://dx.doi.org/10.1016/j.physb.2014.05.055

F. Maiz, Numerical method to calculate the quantum transmission, resonance and eigenvalue energies: application to a biased multibarrier systems, Physica B 463, 93–102, 2015.
http://dx.doi.org/10.1016/j.physb.2015.02.002

Mahmud, M., Islam, M., Hossain, M., Maruf Morshed, M., Improvement of Noise Attenuation in a Duct Using Two Helmholtz Resonators, (2015) International Review of Mechanical Engineering (IREME), 9 (3), pp. 231-236.
http://dx.doi.org/10.15866/ireme.v9i3.5596


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