Structural Engineering and Mechanics

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A general fourth order ordinary differential equation with solution in terms of Bessel functions: theory and engineering applications

  • Attarnejad, Reza (School of Civil Engineering, University of Tehran) ;
  • Ghorbani-Tanha, Amir K. (School of Civil Engineering, University of Tehran)
  • Received : 2005.08.02
  • Accepted : 2007.07.25
  • Published : 2007.12.20
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Abstract

Keywords

References

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  6. Mabie, H.H. and Rogers, C.B. (1968), 'Transverse vibrations of tapered cantilever beams with end supports', J. Acoust. Soc. Am., 44(6), 1739-1741 https://doi.org/10.1121/1.1911327
  7. Mabie, H.H. and Rogers, C.B. (1972), 'Transverse vibrations of double-tapered cantilever beams', J. Acoust. Soc. Am., 51(5), 1771-1774 https://doi.org/10.1121/1.1913028
  8. Mabie, H.H. and Rogers, C.B. (1974), 'Transverse vibrations of double-tapered cantilever beams with end support and with end mass', J. Acoust. Soc. Am., 55(5), 986-991 https://doi.org/10.1121/1.1914673
  9. Watson, G.N. (1958), A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England
  10. Yang, K.Y. (1990), 'The natural frequencies of a non-uniform beam with a tip mass and with translational and rotational springs', J. Sound Vib., 137(2), 339-341 https://doi.org/10.1016/0022-460X(90)90799-6

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