Free vibrations of anisotropic beam

Authors

  • Petr E. Tovstik St.Petersburg State University, Universitetskaya nab., 7-9, St.Petersburg, 199034, Russian Federation;
  • Tatiana P. Tovstik Institute of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;

Abstract

Thin elastic homogeneous beam made of a material of general anisotropy is studied. Earlier to deliver 1D equations of motion the generalized Timoshenko-Reissner hypotheses are used. In this paper the 1D equations and the corresponding boundary conditions of anisotropic beam free vibrations are obtained by the asymptotic expansion of unknowns in series in powers of the relative beam thickness. The zeroes and the first approximations are constructed. The transversal and the longitudinal vibrations are connected, but for the low-frequency vibrations this connection is weak. It is recommended to ignore in a zeroes approximation this connection and to study the transversal and the longitudinal vibrations separately as for an isotropic Bernoulli-Euler beam with the modified Young module which takes anisotropy into account.

Keywords:

beam, free vibrations, general anisotropy

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Published

2014-11-01

How to Cite

Tovstik, P. E., & Tovstik, T. P. (2014). Free vibrations of anisotropic beam. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(4), 599–608. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11093

Issue

Vol. 1 No. 4 (2014)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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