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2014 | 125 | 4A | A-169-A-173
Article title

The Influence of Local Increase of Stress on Eigenvalues for a Simply Supported Beam

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Languages of publication
EN
Abstracts
EN
Local increase of bending stress in a beam may be caused by a decrease of the cross-section (fracture) or a local increase of bending torque. The increase of stress issues from the well known interdependence between the stress, the bending torque and the sectional modulus. The work presents a derivation of differential equations for eigenfunctions in both cases. Knowing the eigenfunctions and boundary conditions we determine a system of algebraic equations for the eigenvalues that are different from the eigenvalues of the beam without local stress disturbances. Two computational models of local increase of stress were constructed: with fracture and with local increase of bending torque.
Keywords
EN
Contributors
author
  • AGH University of Science and Technology, Department of Mechanics and Vibroacoustics, Al. A. Mickiewicza 30, 30-059 Krakow, Poland
author
  • AGH University of Science and Technology, Department of Mechanics and Vibroacoustics, Al. A. Mickiewicza 30, 30-059 Krakow, Poland
References
  • [1] S. Kasprzyk, Acta Phys. Pol. A 121, 981 (2012)
  • [2] M. Wiciak, S. Kasprzyk, Opuscula Math. 27, 245 (2007)
  • [3] M. Jabłonski, A. Ozga, T. Korbiel, P. Pawlik, Acta Phys. Pol. A 119, 971 (2011)
  • [4] F.P. Beer, E.R. Johnson (Jr.), Mechanics for Engineers, Cliffs, New Jersey 1977
  • [5] S. Kasprzyk, R. Marczuk, Acta Physica Polonica A 121, A-191 (2012), doi: Acta Physica Polonica A 121, A-191 (2012)
  • [6] S. Kasprzyk, Dynamics of Continuous Systems. University's Scripts, Wydawnictwo AGH, Kraków 1988, (in Polish)
  • [7] P. Antosik, J. Mikulski, R. Sikorski, Theory of Distributions; the Sequental Approach, Elsevier Sci. Publ., New York 1973
  • [8] J. Mikusiński, R. Sikorski, Elementary Theory of Distribution, PWN, Warszawa 1964
  • [9] L. Schwartz, Mathematics for Physical Sciences, PWN Warszawa 1984
  • [10] S. Kaliski, Technical Mechanics. Waves and Vibrations, PWN, Warszawa 1986
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv125n4a33kz
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