Structural Engineering and Mechanics

  • 제7권1호
  • /
  • Pages.53-67
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  • 1999
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Free vibration analysis of elliptic and circular plates having rectangular orthotropy

  • Chakraverty, S. (Institute of Sound and Vibration Research, University of Southampton) ;
  • Petyt, M. (Institute of Sound and Vibration Research, University of Southampton)
  • 발행 : 1999.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

키워드

참고문헌

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피인용 문헌

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  2. Flexural transient response of elastically supported elliptical plates under in-plane loads using Mathieu functions vol.62, 2013, https://doi.org/10.1016/j.tws.2012.07.022
  3. Effect of elastic foundation on the vibration of orthotropic elliptic plates with varying thickness vol.42, pp.4, 2007, https://doi.org/10.1007/s11012-007-9059-5
  4. Exact vibration solutions for circular Mindlin plates with multiple concentric ring supports vol.39, pp.25, 2002, https://doi.org/10.1016/S0020-7683(02)00494-8
  5. Vibration of circular Mindlin plates with concentric elastic ring supports vol.45, pp.3, 2003, https://doi.org/10.1016/S0020-7403(03)00059-6
  6. The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review 2017, https://doi.org/10.1177/1077546317694724
  7. Vibration of Rectangular Orthotropic Elliptic Plates of Quadratically Varying Thickness Resting on Elastic Foundation vol.126, pp.1, 2004, https://doi.org/10.1115/1.1640654
  8. On the use of GDQ for vibration characteristic of non-homogeneous orthotropic rectangular plates of bilinearly varying thickness vol.226, pp.5, 2015, https://doi.org/10.1007/s00707-014-1272-4
  9. Vibration of non-homogeneous plates using two-dimensional orthogonal polynomials as shape functions in the Rayleigh—Ritz method vol.213, pp.7, 1999, https://doi.org/10.1177/095440629921300706
  10. Vibration of Nonhomogeneous Orthotropic Elliptic and Circular Plates With Variable Thickness vol.129, pp.2, 2007, https://doi.org/10.1115/1.2346695
  11. Dynamics of Rotating Composite Disc vol.7, pp.6, 1999, https://doi.org/10.1007/s42417-019-00155-8