Własności Funkcji Własnych dla Drgań Poprzecznych Belek Jednorodnych z Uwzględnieniem Wpływu Ścinania i Bezwładności Obrotowej

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Authors

  • D. Raskovic

Abstract

This paper contains an analysis of transverse vibrations of homogeneous beams, taking into consideration the influence of shearing and rotational inertia of a cross-section. The method used is that of the calculus of variations. The equation of motion is applied to 25 cases of end support and to most general boundary conditions. For these cases, frequency equations and the properties of the eigenfunctions are discussed. For 16 cases of the free regime (Rayleigh's problem), the roots of the frequency equations tend asymptotically to rational values of the number kr. Kryliv's table of integrals, [2], for steady-state regimes is extended to cover all cases.


References

[1] S. Timoshenko, Vibrations Problems in Engineering, New York 1955.

[2] [in Russian]

[3] R. Weinstock, Calculus of Variations, New York 1952.

[4] W. S. Kimball, Calculus of Variations, London 1952.

[5] Lord Rayleigh, Theory of Sound, New York 1945.