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Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell

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Abstract

In this paper, the axisymmetric vibration of a fluid-filled spherical membrane shell is studied based on nonlocal elasticity theory. The membrane shell is considered elastic, homogeneous and isotropic. The shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The membrane shell is completely filled with an inviscid fluid. The motion of the fluid is governed by the wave equation. Nonlocal governing equations of motion for the fluid-filled spherical membrane shell are derived. Along the contact surface between the membrane and the fluid, the compatibility requirement is applied and Legendre polynomials, associated Legendre polynomials and spherical Bessel functions are used to obtain the natural frequencies of the fluid-filled spherical membrane shells. The frequencies for both empty and fluid-filled spherical membrane shell are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. An excellent agreement is found between the present and previous ones available in the literature. The variations of the natural frequencies with the small-scale parameter, density ratio, wave speed ratio and Poisson’s ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, 71348-51154, Shiraz, Islamic Republic of Iran

    S. Ahmad Fazelzadeh & Esmaeal Ghavanloo

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  1. S. Ahmad Fazelzadeh
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  2. Esmaeal Ghavanloo
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Correspondence to S. Ahmad Fazelzadeh.

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Fazelzadeh, S.A., Ghavanloo, E. Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell. Acta Mech 223, 2011–2020 (2012). https://doi.org/10.1007/s00707-012-0692-2

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  • DOI: https://doi.org/10.1007/s00707-012-0692-2

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