Engineering Transactions, 6, 3, pp. 433-452, 1958

Tłumienie Falami Naprężeń w Belkach Sprężystych

J. Więckowski
Instytut Podstawowych Problemów Techniki PAN

An analogy is indicated between vibrations in elastic bodies and in liquids. In a number of cases of forced vibration of infinite elastic beams, reaction forces of these beams are found. It is pointed out that for a series of cases of harmonic or exponential vibrations, these forces have the form of viscous friction forces with the coefficient of damping depending on the frequency and the constants characterizing the elastic properties and the geometry of the beam. For a certain simple case of forced vibration, the reduced mass of an infinite beam is determined in function of the above constants. The results obtained are illustrated by simple examples of vibration of a harmonic oscillator connected with an infinite elastic beam.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


R. A. Anderson, Wave Groups in Flexural Motion of Beams Predicted by Timoshenko Theory, Journ. Appl. Mech. 4 (1954).

R. A. Anderson, The Wave Method for Selving Flexural Vibration Problems, Journ. Appl. Mech. 4 (1954).

B. A. Boley, C. C. Chao, Some Solutions of the Timoshenko Beam Equations, Journ. Appl. Mech. 5 (1955).

C. Chree, Trans. Camb. Phil. Soc., 14, 1889, 250.

C. Chree, Quart. Journ. Pure Appl. Math., 23, 1899, 335.

M. Goland, P. D. Wickersha m, M. A. Dengler, Propagation of the Elastic Impact in Beams in Bending, Journ. Appl. Mech. 1 (1955).

[in Russian]

[in Russian]

H. Kolsky, Stress Waves in Solids, Oxford 1953.

J. Miklowitz, Propagation of Compresional Waves in Dispersive Elastic Rod, Journ. Appl. Mech. 2 (1957).

L. Pochhammer, Journ. angew. Math., 81, 1876, s. 324.

Rayleigh Lord (J. W. Strett), Theory of Sound.

F. O. Ringle b, Motion and Stress of an Elastic Cable Due to Impact, Journ. Appl. Mech, 3 (1957).

A. Ripperberger, H. Abramson Norman, A Study of the

Propagation of Flexural Waves in Elastic Beams, Journ. Appl. Mech, 3 (1957).

R. Skalak, Longitudinal Impact of a Semi-Infinite Circular Elastic Bar, Journ. Appl. Mech. 1 (1957).

S, P. Timoshenko, Phil. Mag. 41 (1921), 744,

J. Wieckowski, Równania drgań gietnych kadłuba statku [Equations of Flexural Vibration of d Ship Hull], Warszawa 1957.