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# Three Dimensional Vibration Analysis of Rectangular Plates With Undamaged and Damaged Boundaries by the Spectral Collocation Method

[+] Author Affiliations
Ma’en S. Sari, Eric A. Butcher

New Mexico State University, Las Cruces, NM

Paper No. DETC2011-48049, pp. 37-45; 9 pages
doi:10.1115/DETC2011-48049
From:
• ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
• Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
• Washington, DC, USA, August 28–31, 2011
• Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
• ISBN: 978-0-7918-5478-5

## abstract

This paper presents a new numerical technique for the free vibration analysis of isotropic three dimensional elastic plates with damaged boundaries. In the study, it is assumed that the plates have free lateral surfaces, and two opposite simply supported edges, while the other edges could be clamped, simply supported or free. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of three dimensional plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged three dimensional plates indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for damage detection of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

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