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Vibration analysis of bi-layered FGM cylindrical shells

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Abstract

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain–displacement and curvature–displacement relationships are utilized from Love’s first approximation linear thin shell theory. The versatile Rayleigh–Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Sargodha, Sargodha, 40100, Punjab, Pakistan

    Shahid Hussain Arshad, Nazra Sultana & Zafar Iqbal

  2. Department of Mathematics, G C University Faisalabad, Faisalabad, 38000, Punjab, Pakistan

    Muhammad Nawaz Naeem

  3. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Punjab, Pakistan

    Abdul Ghafar Shah

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  1. Shahid Hussain Arshad
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  2. Muhammad Nawaz Naeem
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  3. Nazra Sultana
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  4. Abdul Ghafar Shah
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  5. Zafar Iqbal
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Correspondence to Shahid Hussain Arshad.

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Arshad, S.H., Naeem, M.N., Sultana, N. et al. Vibration analysis of bi-layered FGM cylindrical shells. Arch Appl Mech 81, 319–343 (2011). https://doi.org/10.1007/s00419-010-0409-8

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  • DOI: https://doi.org/10.1007/s00419-010-0409-8

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