Abstract
Equations are obtained for the longitudinal and transverse oscillations of a prismatic rod that differ from the standard equations of structural mechanics (strength of materials). The difference lies both in the appearance of new terms in the equations of motion corresponding to the Timoshenko theory, and in a refinement of the boundary conditions and the conditions on the rigidity of the rod for transverse oscillations. The oscillations of a vertical cantilevered rod when its base moves horizontally from a state of rest are examined and a comparison is made with the classical theory of transverse (bending) oscillations of prismatic rods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. N. Tishchenko, “Oscillations of elastic thin plates, ” Dinam. Sist., 15, pp. 84–91 (1999).
S. P. Timoshenko, A Course in the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (1972).
G. G. Whitham, Linear and Nonlinear Waves [Russian translation], Mir, Moscow (1977).
I. A. Birger andYa. G. Panovko (eds.), Strength, Stability, Oscillations. A Handbook, Vol. 3 [in Russian], Mashinostroenie, Moscow (1968).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tishchenko, V.N. Oscillations of a Prismatic Rod. Journal of Mathematical Sciences 107, 4409–4415 (2001). https://doi.org/10.1023/A:1012508601625
Issue Date:
DOI: https://doi.org/10.1023/A:1012508601625