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Vibration Analysis of the Multiple-Hole Membrane by using the Coupled Diem-Fe Scheme

Published online by Cambridge University Press:  13 August 2015

D.-S. Liu  and
I.-H. Lin
D.-S. Liu*
Affiliation:
Department of Mechanical Engineering, National Chung Cheng University, Chiayi, Taiwan
I.-H. Lin
Affiliation:
Advanced Institute of Manufacturing with High-Tech Innovations, National Chung Cheng University, Chiayi, Taiwan
*
* Corresponding author ([email protected])
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Abstract

This paper presents a 2D dynamics infinite element method (DIEM) for modeling the multiple-hole membrane for vibration analysis. A new concept involving converting the DIEM into a super element that can adjust the hole size and free and fixed boundary conditions around the hole is also proposed. The special element, embedded with an elastic membrane, is formulated on the basis of the conventional finite element method (FEM) by using the similarity mass/stiffness property of isoparametric elements and Craig-Bampton matrix reduction procedures. A DIEM-FE coupling scheme is also developed and self-programmed into the software MATLAB to conduct the vibration analysis of a membrane with multiple holes. The DIEM-FE approach is validated to study the vibration of the rectangular membranes by using the corresponding analytical solutions and the solutions obtained using the conventional FEM. The DIEM-FE is then applied to analyze imbedded L-shaped and circular opening problems. The effects of varying hole diameters and the free or fixed boundary condition along the hole are also examined. Finally, the last example shows that to perform vibration analysis of the multiple-hole membrane, only one DIEM mass/stiffness matrix must be calculated for all holes with an identical circular shape. Overall, this study provides a flexibility and efficient scheme for analyzing a wide variety of membrane vibration problems. The number of degrees of freedom and the corresponding PC memory storage are substantially reduced through the computation.

Keywords

Infinite element methodFinite element methodCraig-Bampton reduction methodMembrane vibration analysis
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 2 , April 2016 , pp. 163 - 173
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

1.Houmat, A., “Hierarchical Finite Element Analysis of the Vibration of Membranes,” Journal of Sound and Vibration, 201, pp. 465–472 (1997).Google Scholar
2.Houmat, A., “A Triangular Fourier P-Element for the Analysis of Membrane Vibrations,” Journal of Sound and Vibration, 230, pp. 31–43 (2000).Google Scholar
3.Houmat, A., “A Sector Fourier P-Element for Free Vibration Analysis of Sectorial Membranes,” Computers & Structures, 79, pp. 1147–1152 (2001).CrossRefGoogle Scholar
4.Houmat, A., “Free Vibration Analysis of Membranes Using the H-P Version of the Finite Element Method,” Journal of Sound and Vibration, 282, pp. 401–410 (2005).Google Scholar
5.Houmat, A., “Free Vibration Analysis of Arbitrarily Shaped Membranes Using the Trigonometric P-Version of the Finite-Element Method,” Thin-Walled Structures, 44, pp. 943–951 (2006).Google Scholar
6.Kang, S. W., Lee, J. M. and Kang, Y. J., “Vibration Analysis of Arbitrarily Shaped Membranes Using Non-Dimensional Dynamic Influence Function,” Journal of Sound and Vibration, 221, pp. 117–132 (1999).CrossRefGoogle Scholar
7.Kang, S. W. and Lee, J. M., “Application of Free Vibration Analysis of Membranes Using the Non-Dimensional Dynamic Influence Function,” Journal of Sound and Vibration, 234, pp. 455–470 (2000).Google Scholar
8.Kang, S. W. and Lee, J. M., “Free Vibration Analysis of an Unsymmetric Trapezoidal Membrane,” Journal of Sound and Vibration, 272, pp. 450–460 (2004).Google Scholar
9.Kang, S. W., Atluri, S. N. and Kim, S. H., “Application of the Nondimensional Dynamic Influence Function Method for Free Vibration Analysis of Arbitrarily Shaped Membranes,” Journal of Vibration and Acoustics-Transactions of the ASME, 134, pp. 041008-1–041008-8 (2012).Google Scholar
10.Guo, Z. H., “Similar Isoparametric Elements,” Science Bulletin, 24, pp. 577–582 (1979).Google Scholar
11.Ying, L. A., “An Introduction to Infinite Element Method.,” Mathematics in Practice Theory, 2, pp. 69–78 (1992).Google Scholar
12.Liu, D. S. and Chiou, D. Y., “A Coupled IEM/FEM Approach for Solving Elastic Problems with Multiple Cracks,” International Journal of Solids and Structures, 40, pp. 1973–1993 (2003).Google Scholar
13.Liu, D. S., Chiou, D. Y. and Lin, C. H., “3D IEM Formulation with an IEM/FEM Coupling Scheme for Solving Elastostatic Problems,” Advances in Engineering Software, 34, pp. 309–320 (2003).Google Scholar
14.Liu, D. S. and Chiou, D. Y., “2-D Infinite Element Modeling for Elastostatic Problems with Geometric Singularity and Unbounded Domain,” Computers & Structures, 83, pp. 2086–2099 (2005).Google Scholar
15.Liu, D. S. and Chiou, D. Y., “Modeling of Inclusions with Interphases in Heterogeneous Material Using the Infinite Element Method,” Computational Materials Science, 31, pp. 405–420 (2004).Google Scholar
16.Liu, D. S., Chiou, D. Y. and Lin, C. H., “A Hybrid 3D Thermo-Elastic Infinite Element Modeling for Area-Array Package Solder Joints,” Finite Elements in Analysis and Design, 40, pp. 1703–1727 (2004).CrossRefGoogle Scholar
17.Liu, D. S., Chen, C. Y. and Chiou, D. Y., “3-D Modeling of a Composite Material Reinforced with Multiple Thickly Coated Particles Using the Infinite Element Method,” CMES-Computer Modeling in Engineering & Sciences, 9, pp. 179–191 (2005).Google Scholar
18.Liu, D. S., Zhuang, Z. W., Chung, C. L. and Chen, C. Y., “Modeling of Moisture Diffusion in Heterogeneous Epoxy Resin Containing Multiple Randomly Distributed Particles Using Hybrid Moisture Element Method,” CMC-Computers Materials & Continua, 13, pp. 89–113 (2009).Google Scholar
19.Liu, D. S., Zhuang, Z. W., Lyu, S. R., Chung, C. L. and Lin, P. C., “Modeling of Moisture Diffusion in Permeable Fiber-Reinforced Polymer Composites Using Heterogeneous Hybrid Moisture Element Method,” CMC-Computers Materials & Continua, 26, pp. 111–136 (2011).Google Scholar
20.Liu, D. S., Fong, Z. H., Lin, I. H. and Zhuang, Z. W., “Modeling of Moisture Diffusion in Permeable Particle-Reinforced Epoxy Resins Using Three-Dimensional Heterogeneous Hybrid Moisture Element Method,” CMES-Computer Modeling in Engineering & Sciences, 93, pp. 441–468 (2013).Google Scholar
21.Liu, D. S., Tu, C. Y. and Chung, C. L., “Eigenvalue Analysis of Mems Components with Multi-Defect Using Infinite Element Method Algorithm,” CMC-Computers Materials & Continua, 28, pp. 97–120 (2012).Google Scholar
22.Guyan, R. J., “Reduction of Stiffness and Mass Matrices,” AIAA Journal, 3, pp. 380–380 (1965).CrossRefGoogle Scholar
23.Bampton, M. C. C. and Craig, J. R. R., “Coupling of Substructures for Dynamic Analyses,” AIAA Journal, 6, pp. 1313–1319 (1968).Google Scholar
24.Bathe, K.-J., Finite Element Procedures, Klaus-Jurgen Bathe (2006).Google Scholar
25.Kwon, Y. W. and Bang, H., The Finite Element Method Using Matlab, CRC press, Boca Raton (2000).Google Scholar
26.Fox, L., Henrici, P. and Moler, C., “Approximations and Bounds for Eigenvalues of Elliptic Operators,” SIAM Journal on Numerical Analysis, 4, pp. 89–102 (1967).Google Scholar