Research Papers

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

[+] Author and Article Information
M. A. Malkov

Russian Research Center for
Artificial Intelligence,
2-Voikovskiy pr. 1/6,
Moscow 125171, Russia
e-mail: mamalkov@gmail.com

Manuscript received July 15, 2013; final manuscript received November 11, 2013; accepted manuscript posted November 15, 2013; published online December 13, 2013. Assoc. Editor: Bo S G Janzon.

J. Appl. Mech 81(5), 051009 (Dec 13, 2013) (7 pages) Paper No: JAM-13-1286; doi: 10.1115/1.4026026 History: Received July 15, 2013; Revised November 11, 2013; Accepted November 12, 2013

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

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Topics: Waves
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Scalak, R., 1957, “Longitudinal Impact of a Semi-Infinite Circular Elastic Bar,” ASME J. Appl. Mech., 34, pp. 59–64.
Malkov, M. A., 1963, “Two-Dimension Problem of Elastic Impact of Bars,” Dokl. Akad. Nauk SSSR, 148(4), pp. 782–785 (in Russian).
Malkov, M. A., 2013, “Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Short Time Solution,” ASME J. Appl. Mech., 80(1), p. 011023. [CrossRef]
Smirnov, V. I., and Sobolev, S. L., 1932, “New Method of Solution for Plane Problem of Elastic Vibration,” Tr. Seismol. Inst., 20, pp. 1–31 (in Russian).
Malkov, M. A., 1968, “Asymptotic of Two-Dimension Problem of Elastic Impact of Bars,” Appl. Math. Mech., 32(3), pp. 467–471 (in Russian).


Grahic Jump Location
Fig. 1

Breakup and propagation of discontinuity lines after bar collision




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