The problem on the normal impact of an elastic sphere upon an elastic Timoshenko arbitrary cross section thin-walled beam of open section is considered. The process of impact is accompanied by the dynamic flexure and torsion of the beam, resulting in the propagation of plane flexural-warping and torsional-shear waves of strong discontinuity along the beam axis. In addition, the process of impact is accompanied by large transverse deformations and large deflection of the beam in the place of impact, with the consequent generation of longitudinal shock waves and large membrane contractive (tensile) forces. Behind the wave fronts up to the boundaries of the contact region (the beam part with the contact spot), the solution is constructed in terms of one-term ray expansions. During the impact, the sphere moves under the action of the contact force which is determined due to the Hertz’s theory, but the contact region moves under the attraction of the contact force, as well as the twisting and bending-torsional moments and transverse and membrane forces, which are applied to the lateral surfaces of the contact region. Simultaneous consideration of the equations of sphere and the contact region motion leads to the Abel equation of the second kind, wherein the value characterizing the sphere and beam drawing together and the rate of change of this value are used as the independent variable and the function, respectively. The solution to the Abel equation written in the form of a series allows one to determine all characteristics of the shock interaction of the sphere and beam.
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November 1999
Research Papers
The Impact of a Sphere on a Timoshenko Thin-Walled Beam of Open Section With due Account for Middle Surface Extension
Yu. A. Rossikhin,
Yu. A. Rossikhin
Voronezh State Academy of Construction and Architecture, Department of Theoretical Mechanics, ul.Kirova 3-75, Voronezh 394018, Russia
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M. V. Shitikova
M. V. Shitikova
Voronezh State Academy of Construction and Architecture, Department of Theoretical Mechanics, ul.Kirova 3-75, Voronezh 394018, Russia
Search for other works by this author on:
Yu. A. Rossikhin
Voronezh State Academy of Construction and Architecture, Department of Theoretical Mechanics, ul.Kirova 3-75, Voronezh 394018, Russia
M. V. Shitikova
Voronezh State Academy of Construction and Architecture, Department of Theoretical Mechanics, ul.Kirova 3-75, Voronezh 394018, Russia
J. Pressure Vessel Technol. Nov 1999, 121(4): 375-383 (9 pages)
Published Online: November 1, 1999
Article history
Received:
October 19, 1998
Revised:
August 4, 1999
Online:
February 11, 2008
Citation
Rossikhin, Y. A., and Shitikova, M. V. (November 1, 1999). "The Impact of a Sphere on a Timoshenko Thin-Walled Beam of Open Section With due Account for Middle Surface Extension." ASME. J. Pressure Vessel Technol. November 1999; 121(4): 375–383. https://doi.org/10.1115/1.2883718
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