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The Scientific World Journal
Volume 2014 (2014), Article ID 427879, 8 pages
Research Article

Free Vibration Analysis of Patch Repaired Plates with a Through Crack by -Convergent Layerwise Element

Department of Civil Engineering, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 712-749, Republic of Korea

Received 7 February 2014; Accepted 9 June 2014; Published 17 August 2014

Academic Editor: José R. d’Almeida

Copyright © 2014 Jae S. Ahn et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The high-order layerwise element models have been used for damaged plates and shells in the presence of singularities such as crack, cutout, and delamination. In this study, the extension of a proposed finite element model has been tested for free vibration analysis of composite laminated systems. For the elements, three-dimensional displacement fields can be captured by layer-by-layer representation. For the elements, higher-order shape functions are derived by combination of one- and two-dimensional shape functions based on higher-order Lobatto shape functions, not using pure higher-order three-dimensional shape functions. The present model can relieve difficulty of aspect ratios in modeling very thin thickness of bonding layer. For verification of the model, natural frequencies and corresponding mode shapes are calculated and then compared with reference values for uncracked and cracked plates. Also, the vibration characteristics of one-sided patch repaired plates with a through internal crack are investigated with respect to variation of crack length, size and thickness of patch, and shear modulus of adhesive, respectively.