Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Eigenvalue Analysis of Arbitrarily Shaped, Concave Membranes With a Deep Groove Using a Sub-domain Method

영역 분할법을 이용한 깊은 홈을 가진 임의 형상 오목 멤브레인의 고유치 해석

  • 강상욱 (한성대학교 기계시스템공학과) ;
  • 윤주일 (한성대학교 기계시스템공학과)
  • Published : 2009.10.20
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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.

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References

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