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Free vibrations of an isotropic nonhomogeneous infinite plate of linearly varying thickness

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Sommario

Viene considerato il problema delle vibrazioni flessionali libere di una lastra infinita, isotropa, non omogenea, di spessore variabile. L'equazione del moto è stata risolta col metodo di Frobenius, esprimendo lo spostamento mediante sviluppo in serie. Sono state calcolate le prime due au to frequenze per varie combinazioni delle condizioni ai limiti e per differenti valori dei parametri caratteristici della variazione di spessore e della disomogeneità.

Summary

The free transverse vibrations of an isotropic nonhomogeneous infinite plate of variable thickness have been studied on the basis of classical plate theory. The governing differential equation of motion has been solved by Frobenius method by expressing the transverse displacement as an infinite series. The frequencies corresponding to the first two modes of vibration are computed for different values of thickness variation constant, nonhomogeneity parameter, and different combinations of boundary conditions.

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References

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Authors and Affiliations

  1. University of Roorkee, Roorkee, India

    J. S. Tomar (Professor of Applied Mathematics)

  2. J.V. Jain College, Saharanpur, India

    D. C. Gupta (Lecturer of Mathematics) & N. C. Jain (Lecturer of Physics)

Authors
  1. J. S. Tomar
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  2. D. C. Gupta
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  3. N. C. Jain
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Tomar, J.S., Gupta, D.C. & Jain, N.C. Free vibrations of an isotropic nonhomogeneous infinite plate of linearly varying thickness. Meccanica 18, 30–33 (1983). https://doi.org/10.1007/BF02156098

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  • DOI: https://doi.org/10.1007/BF02156098

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