Propagation of Axisymmetric Transients in a Rod
Publication: Journal of Engineering Mechanics
Volume 113, Issue 6
Abstract
The propagation of axisymmetric transients in a rod, governed by the Mindlin‐McNiven theory, is treated by the method of wave‐front expansion. The transients are due to impulsive‐end loading specified in the form of stress, strain, velocity, or acceleration boundary conditions. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variable and its derivatives. These discontinuities are determined from a set of recurrence relations, which are in turn generated using time‐harmonic asymptotic series solutions to the equations of motion. Discontinuities of all orders are determined and the transient solution obtained as a series expansion behind the wave front. The entire solution procedure has been programmed and requires a minimum of input data. Numerical examples are presented to illustrate the method and the results are discussed. Distortion of the transient waves is clearly seen from the results where axial force, strain, velocity, and acceleration responses are presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Achenbach, J. D., Wave Propagation in Elastic Solids, North Holland Publishing Company, Amsterdam, The Netherlands, 1973.
2.
Clough, R. W., and Penzien, J., Dynamics of Structures, Chap. 19, McGraw Hill, New York, N.Y., 1975.
3.
Cohen, H., “Wave Propagation in Elastic Plates,” Journal of Elasticity, Vol. 6, 1976, pp. 245–259.
4.
Friedlander, F. G., Sound Pulses, Cambridge University Press, Cambridge, U.K., 1958.
5.
Graff, K. F., Wave Motion in Elastic Solids, Clarendon Press, Oxford, U.K., 1975.
6.
Havelock, J. H., The Propagation of Disturbances in Dispersive Media, Stechart‐Hafner Service Agency, New York, N.Y., 1964.
7.
Karal, F. C., and Keller, J. B., “Elastic Wave Propagation in Homogenous and Inhomogeneous Media,” Journal of the Acoustical Society of America, Vol. 31, 1959, pp. 694–705.
8.
Kaul, R. K., and McCoy, J. J., “Propagation of Axisymmetric Waves in a Circular Semiinfinite Elastic Rod,” Journal of the Acoustical Society of America, Vol. 36, No. 4, 1964, pp. 653–660.
9.
Kline, M., and Kay, I., Electromagnetic Theory and Geometrical Optics, Wiley Interscience, New York, N.Y., 1965.
10.
McNiven, H. D., and Mengi, Y., “Transient Response in a Rod in Terms of Power Series Expansions,” Journal of Sound and Vibration, Vol. 21, No. 1, 1972, pp. 11–18.
11.
Mengi, Y., and McNiven, H. D., “Analysis of the Transient Excitation of an Elastic Rod by the Method of Characteristics,” International Journal of Solids and Structures, Vol. 6, 1970, pp. 871–892.
12.
Mindlin, R. D., and McNiven, H. D., “Axially Symmetric Waves in Elastic Rods,” Journal of Applied Mechanics, ASME, Vol. 82, 1960, pp. 145–151.
13.
Thambiratnam, D. P., Shah, A. H., and Cohen, H., “Axisymmetric Transients in Shells of Revolution,” Earthquake Engineering and Structural Dynamics, Vol. 3, 1979, pp. 369–382.
14.
Thambiratnam, D. P., “Transient Response of Beam under Initial Stress,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 10, 1984, pp. 1544–1555.
15.
Thambiratnam, D. P., “Transient Waves in a Rod Subjected to Impulsive End Loading,” Earthquake Engineering and Structural Dynamics, Vol. 14, 1986, pp. 475–485.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 113 • Issue 6 • June 1987
Pages: 843 - 860
Copyright
Copyright © 1987 ASCE.
History
Published online: Jun 1, 1987
Published in print: Jun 1987
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.