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The general solution to the classical problem of the finite Euler-Bernoulli beam

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Summary

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Zusammenfassung

Eine analytische Lösung wird angegeben für das Problem der freien und erzwungenen Schwingungen eines endlichen Euler-Bernoulli-Balkens bei beliebigen (teilweise fixierten) Randbedingungen. Die Einflüsse einer linearen Reibungsdämpfung, der Winkler-Einbettung, einer konstanten axialen Spannung, der konzentrierten Massen, sowie von beliebigen Anregungsfunktionen werden in der Lösung berücksichtigt. Es werden keine Einschränkungen bezüglich der Parameter des Problems angenommen, und die Lösung enthält alle früheren zitierten Lösungen als besondere Fälle.

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References

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Author notes

  1. C. L. Amba-Rao

    Present address: Vikram Sarabhai Space Center, Trivandrum, India

Authors and Affiliations

  1. NASA Ames Research Center, Moffet Field, California, USA

    M. Y. Hussaini & C. L. Amba-Rao

Authors
  1. M. Y. Hussaini
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  2. C. L. Amba-Rao
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Hussaini, M.Y., Amba-Rao, C.L. The general solution to the classical problem of the finite Euler-Bernoulli beam. Journal of Applied Mathematics and Physics (ZAMP) 29, 704–710 (1978). https://doi.org/10.1007/BF01601496

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  • DOI: https://doi.org/10.1007/BF01601496

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