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VIBRATIONS OF DAMAGED 1D-3D MULTI-STRUCTURES

  • Adolf G. Aslanyan
  • Janusz Dronka
  • Gennady S. Mishuris
  • Özgür Selsil
Conference paper
  • 1.3k Downloads
Part of the Springer Proceedings in Physics book series (SPPHY, volume 111)

Abstract

The objective of the paper is to study the vibrations of 1D-3D nondegenerate multistructures, which are partly damaged. Such an analysis is useful to quickly asses the condition of a structure which has been in use over a long period of time. We look at three different positions of damage: top, middle or bottom of one leg. We calculate six eigenfrequencies associated with rigid body motion of the 3D structure and derive simple analytical asymptotic formulae for these eigenfrequencies. Hence, we analyse the effect of weakening of a leg. Accuracy of the asymptotic formulae is also checked with 3D finite element computations.

Keywords

Asymptotic Formula Rigid Body Motion Damage Parameter Elastic Shell Rigid Body Translation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aslanyan, A. G., Movchan, A. B., Selsil, O. (2002) Vibrations of multi-structures including elastic shells: Asymptotic analysis. Euro. Jnl of Applied Mathematics 11, 109–128.CrossRefMathSciNetGoogle Scholar
  2. Aslanyan, A. G., Movchan, A. B., Selsil, O. (2003) Estimates for the low eigenfrequencies of a multi-structure including an elastic shell. Euro. Jnl of Applied Mathematics 14, 313–342.CrossRefMathSciNetGoogle Scholar
  3. Aslanyan, A.G., Movchan, A.B., Selsil, O. (2003) Asymptotics for the first six eigenfrequencies of a 1D-3D multi-structure. Proceedings of IUTAM international symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Liverpool, UK, 221–228.Google Scholar
  4. Aslanyan, A.G., Dronka, J., Mishuris, G.S., Selsil, O. (2005) Vibrations of a weakly nondegenerate 1D-3D multi-structure. Submitted for publication to Archives of Mechanics.Google Scholar
  5. Aslanyan, A.G., Dronka, J., Mishuris, G.S., Selsil, O. (2005) The effect of structural damage on the vibrations of 1D-3D multi-structures. Proceedings of IIIrd Syposium on Damage in Materials and Structures, Augustow, Poland, 11–14.Google Scholar
  6. Kozlov, V.A., Maz’ya, V.G., Movchan, A.B. (1999) Asymptotic analysis of fields in multistructures, Oxford University Press.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Adolf G. Aslanyan
    • 1
  • Janusz Dronka
    • 2
  • Gennady S. Mishuris
    • 2
  • Özgür Selsil
    • 3
  1. 1.Druzhba St. 5, kv. 355, Khimki, Moscow RegionRussia
  2. 2.Dept. of MathematicsRzeszów Univ. of Tech.RzeszówPoland
  3. 3.Dept. of Mathematical SciencesThe Univ. of LiverpoolLiverpoolUK

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