Resonance Frequency of Acoustic Eccentric Hollow Sphere

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mme.modares.ac.ir

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Resonance Frequency of Acoustic Eccentric Hollow Sphere

Yaser Mirzaei

^1*

Seyyed Mohammad Hasheminejad

²

Hessam Mousavi-Akbarzadeh

³

1-Department of Mechanical Engineering, Islamic Azad University, Damavand, Iran.

2-Department of Mechanical Engineering, Iran University of Science and Technology, Tehran,Iran.

3-Department of Mechanical Engineering, Islamic Azad University, Eslamshahr, Iran P.O.B. 194/39715 Damavand, Iran, [email protected]

A RTICLE I NFORMATION A BSTRACT

Original Research Paper Received 05 January 2015 Accepted 09 February 2015 Available Online 04 April 2015

An exact three-dimensional elastodynamic analysis for describing the acoustic resonance frequencies of an acoustic eccentric hollow sphere is derived. The Neumann boundary conditions for inner and outer sphere are considered. The translational addition theorem for spherical vector wave functions is employed to enforce Neumann boundary conditions. The frequency equations in the form of exact determinantal equations involving spherical Bessel functions and Wigner 3j symbols are obtained. Due to geometric symmetry for spherical cavity with inner concentric sphere, multiple degenerate acoustic resonance frequencies occurred. According to the geometry parameters and frequency number, introduction of eccentricity has different effect on the acoustic resonance frequency shift. Extensive numerical results have been carried out for acoustic resonance frequency of selected inner-outer radii ratios in wide range of cavity eccentricities. The numerical results describe the imperative influence of cavity eccentricity and radii ratio on the resonance frequency of the acoustic hollow sphere. Some phenomena such as diminishing degenerate resonance frequency, increase in the number of resonant frequencies through the splitting of degenerate modes and exchanging the mode of resonance frequencies are demonstrated and discussed.

Keywords:

Resonance Frequency Acoustic

Eccentric Hollow Sphere

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