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Natural Vibration with Damping Proportional to a Power of the Velocity

Published online by Cambridge University Press:  04 July 2016

P. D. Richardson
P. D. Richardson*
Affiliation:
Division of Engineering, Brown University, Providence, R.I., U.S.A.
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Summary

In a recent note in the Journal, Morley and Bryce discuss the problem of natural vibration with a damping force proportional to a power of the velocity. They address themselves particularly to the problem of interpreting experimental measurements, and mention an application of the study of an elasticity in metals. They were apparently unaware of previous analytic studies of this problem, and their analysis is somewhat inaccurate in indicating that the full-cycle logarithmic decrement rather than the half-cycle logarithmic decrement characterises the damping.

It is intended here to outline the previous analytic studies, to present the essential results, including those which can be directly employed in the interpretation of amplitude measurements, and to mention typical applications.

Type
Technical notes
Information
The Aeronautical Journal , Volume 68 , Issue 648 , December 1964 , pp. 846 - 849
Copyright
Copyright © Royal Aeronautical Society 1964

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References

1.Morley, A. W. and Bryce, W. D.Natural Vibration with Damping Force Proportional to a Power of the Velocity. Journal of the Royal Aeronautical Society, Vol. 67, p. 381, June 1963.Google Scholar
2.Iacobsen, L. S.On a General Method of Solving Second- Order Ordinary Differential Equations by Phase-Plane Displacement. Transactions American Society Mechanical Engineers, Journal of Applied Mechanics, Vol. 19, p. 543, 1952.CrossRefGoogle Scholar
3.Andronoff, A. A. and Chaikin, C. E.Theory of Oscillations. Princeton Univ. Press, Princeton, N.J., 1949.Google Scholar
4.Kryloff, N. and Bogoliuboff, N.Introduction to Non- Linear Mechanics. Princeton Univ. Press, Princeton, N.J., 1943.Google Scholar
5.Klotter, K.The Attenuation of Damped Free Vibrations and the Derivation of the Damping Law from Recorded Data. Proceedings, Second U.S. National Congress of Applied Mechanics, p. 85, 1954.Google Scholar
6.Richardson, P. D.Free Oscillations with Small Non-Linear Damping. Transactions American Society Mechanical Engineers, Journal of Basic Engineering, Vol. 84, p. 413, 1962.Google Scholar
7.Van zandt, J. P.Oscillating Systems Damped by Resistance Proportional to the Square of the Velocity. Physical Review, Second Series, Vol. 10, p. 415, 1917.Google Scholar
8.Milne, W. E.Damped Vibrations. University of Oregon Publications, Vol. 2, No. 2, 1923.Google Scholar
9.Richardson, P. D.Free Oscillations with Damping Pro portional to the Square of the Velocity. Applied Scientific Research A, Vol. 11, p. 397, May 1963.CrossRefGoogle Scholar
10.Milne, W. E.Tables of Damped Vibrations. University of Oregon Publications, Mathematical Series, Vol. 1, No 1, March 1929.Google Scholar
11.Wilson, E. B.An Introduction to Scientific Research. McGraw-Hill Publ. Co., New York, Chap. 8, 1952.Google Scholar
12.Richardson, P. D.Comments on Viscous Damping in Oscillating Liquid Columns. International Journal of Mech anical Sciences, Vol. 5, p. 415, 1963.Google Scholar
13.Holtzmark, J., Johnsen, I., Slkkeland, T. and Skavlem, S.Boundary Layer Flow Near a Cylindrical Obstacle in an Oscillating Incompressible Fluid. Journal Acoustical Society of America, Vol. 26, p. 26, January 1954.Google Scholar