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http://dx.doi.org/10.5050/KSNVN.2009.19.10.1069

Eigenvalue Analysis of Arbitrarily Shaped, Concave Membranes With a Deep Groove Using a Sub-domain Method  

Kang, S.W. (한성대학교 기계시스템공학과)
Yoon, J.I. (한성대학교 기계시스템공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.19, no.10, 2009 , pp. 1069-1074 More about this Journal
Abstract
A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.
Keywords
Eigenvalues; Sub-domain Method; NDIF Method; Free Vibration; Concave Membrane; Arbitrarily Shaped Membrane; Deep Groove;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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