Engineering Transactions, 29, 3, pp. 427-437, 1981

On the longitudinal Vibrations of Tapered Bars

D.S. Chehil
Department of Applied Mathematics, Nova Scotia Technical College, Halifax, N.S.
Canada

R.S. Dhaliwal
Department of Mathematics and Statics, The University of Calgary, Calgary, Alberta
Canada

In this paper an attempt is made to improve the elementary theory that describes the longitudinal vibrations of a tapered rod. The differential equation including both lateral inertia and shear is derived. In order to facilitate comparison with the known results, numerical values of the fundamental resonant frequencies and velocity gain factors are obtained for conical bars with linear taper.
Full Text: PDF

References

D. S. CHEHIL, H. S. HEAPS, Effect of lateral motion on the longitudinal vibration of tapered bars, J. of the Acoust. Soc. of America, 43, 3, 540-544, March 1968.

L. T. RUSSELL, H. S. HEAPS, Family of cylindrical velocity transformers; study by Analog Computer Techniques, J. of the Acoust. Society of America, 38, 47-49, 1965.

A. MOHAMMED, Equivalent circuits of solid horns undergoing longitudinal vibrations, J. of the Acoust. Society of America, 38, 862-866, 1965.

R. E. D. BISHOP, Longitudinal waves in beams, The Aeronaut. Quart., III, February 1952.

G. E. MARTIN, On the propagation of longitudinal stress waves infinite solid elastic horns, The University of Texas, Ph. D., Engineer. Mech., 1966.

S. TIMOSHENKO, Vibration problems in engineering, D. Van Nostrand Company, Inc., November 1954.

L. G. MERKULOV, Design of ultrasonic concentrators, Soviet Phys., Acoust. 3, 246-255, 1957.

F. J. YOUNG, Family of bars of revolution in longitudinal half-wave resonance, J. of the Acoust. Society of America, 32, 1263-1264, 1960.

E. EISNER, Resonant vibration of a cone, J. of the Acoust. Society of America, 36, 309-312, 1964.

E. EISNER, Complete solutions of the Webster Horn equation, J. of the Acoust. Society of America, 41, 1126-1146, 1967.

J. W. STRUTT LORD RAYLEIGH, Theory of sound, Dover Publications, Inc., 1, 157, New York 1945.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland