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

• Authors: S. Kasprzyk , R. Marczuk
• 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

46.70.De; 46.40.-f

Discipline

• 46.40.-f: Vibrations and mechanical waves(see also 43.40.+s Structural acoustics and vibration; 62.30.+d Mechanical and elastic waves; vibrations in mechanical properties of solids)
• 46.70.De: Beams, plates, and shells

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 125
• Issue: 4A
• Pages: A-169-A-173

Dates

published

2014-04

Contributors

author

S. Kasprzyk

• AGH University of Science and Technology, Department of Mechanics and Vibroacoustics, Al. A. Mickiewicza 30, 30-059 Krakow, Poland

author

R. Marczuk

• 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

Identifiers

DOI

10.12693/APhysPolA.125.A-169