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A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations

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Abstract

Free vibration analysis of functionally graded sandwich beams with general boundary conditions and resting on a Pasternak elastic foundation is presented by using strong form formulation based on modified Fourier series. Two types of common sandwich beams, namely beams with functionally graded face sheets and isotropic core and beams with isotropic face sheets and functionally graded core, are considered. The bilayered and single-layered functionally graded beams are obtained as special cases of sandwich beams. The effective material properties of functionally graded materials are assumed to vary continuously in the thickness direction according to power-law distributions in terms of volume fraction of constituents and are estimated by Voigt model and Mori–Tanaka scheme. Based on the first-order shear deformation theory, the governing equations and boundary conditions can be obtained by Hamilton’s principle and can be solved using the modified Fourier series method which consists of the standard Fourier cosine series and several supplemented functions. A variety of numerical examples are presented to demonstrate the convergence, reliability and accuracy of the present method. Numerous new vibration results for functionally graded sandwich beams with general boundary conditions and resting on elastic foundations are given. The influence of the power-law indices and foundation parameters on the frequencies of the sandwich beams is also investigated.

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Authors and Affiliations

  1. College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Zhu Su, Guoyong Jin & Xinmao Ye

  2. Heilongjiang Institute of Technology, Harbin, 150050, People’s Republic of China

    Yunlong Wang

Authors
  1. Zhu Su
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  2. Guoyong Jin
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  3. Yunlong Wang
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  4. Xinmao Ye
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Correspondence to Guoyong Jin.

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Su, Z., Jin, G., Wang, Y. et al. A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations. Acta Mech 227, 1493–1514 (2016). https://doi.org/10.1007/s00707-016-1575-8

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  • DOI: https://doi.org/10.1007/s00707-016-1575-8

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