3-D Vibration Analysis Of The Rectangular Micro Damaged Plates

  • Ahmet KiriŞ
  • Esİn İnanEmail author
Part of the Springer Proceedings in Physics book series (SPPHY, volume 126)

In the present work, damaged plates are modeled by the micro-elongation theory which neglects the micropolar effects in Eringen's microstretch theory. The wave propagation problem is studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the micro-structure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.


microelongation theory micro damaged plate natural frequencies 


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  1. 1.
    A. C. Eringen, 1990. Theory of thermo-microstretch elastic solids, International Journal of Engineering Science, 28, 1291–1301.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    B. Singh, R. Kumar, 1998. Wave propagation in a generalized thermo-microstretch elastic solid, International Journal of Engineering Science, 36 891–912.CrossRefMathSciNetGoogle Scholar
  3. 3.
    D. Zhou, Y. K. Cheung, F. T. K. Au, S. H. Lo, 2002. Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method, International Journal of Solids and Structures, 39, 6339–6353.zbMATHCrossRefGoogle Scholar

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© Springer Science + Business Media B.V 2008

Authors and Affiliations

  1. 1.Faculty of Science and LettersIstanbul Technical UniversityMaslakTurkey
  2. 2.Faculty of Arts and SciencesIşk UniversityMaslakTurkey

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