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Transverse vibration of rectangular plates elastically supported at points on edges

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Abstract

This paper studies transverse vibration of rectangular plates with two opposite edges simply supported, other two edges arbitrarily supported and free edges elastically supported at points. A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular plates elastically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourier series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given. Inherent frequencies and mode shape with any accuracy can be gained.

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References

  1. Cox, H. L. and J. Boxer, Vibration of rectangular plates point-supported at corners,Aeronautical Quarterly.11 (1960).

  2. Reed, R. E., Comparison of methods in calculating frequencies of corner-supported rectangular plates, NASA TN D-3030 (1965).

  3. Kirk, C. L., A note on the lowest natural frequency of square plate point-supported at the corners,J. the Royal Aeronautical Society,66 (1962).

  4. Kerstens, L. G. M., Vibration of a rectangular plate supported at an arbitrary number of points,J. Sound and Vibration,65 (1979).

  5. Gorman, D. J., Free vibration analysis of rectangular plates with symmetrically distributed point supports along the edges,J. Sound and Vibration,73 (1980).

  6. Gorman, D. J., An analytical solution for the free vibration analysis of rectangular platess resting on symmetric point supports,J. Sound and Vibration.79 (1981).

  7. Gorman, D. J.,Vibration of Rectangular Plates, New York, Elsevier North Holland (1982).

    Google Scholar 

  8. Bapat, A. V. and N. Venkatramani, A new approach for the representation of a point support in the analysis of plates,J. Sound and Vibration,120 (1988).

  9. Bapat, A. V. and N. Venkatramani, Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates,J. Sound and Vibration,120 (1988).

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Authors and Affiliations

  1. East China Institute of Technology, Nanjing

    Zhou Ding

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  1. Zhou Ding
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Communicated by Pan Li-zhou

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Ding, Z. Transverse vibration of rectangular plates elastically supported at points on edges. Appl Math Mech 10, 979–987 (1989). https://doi.org/10.1007/BF02017523

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  • DOI: https://doi.org/10.1007/BF02017523

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