Open Access

ARTICLE

Eigenvalue Analysis of MEMS Components with Multi-defect using Infinite Element Method Algorithm

by De-Shin Liu¹, Chin-Yi Tu¹, Cho-Liang Chung³

1 Advanced Institute of Manufacturing for High-tech Innovations and Department of Mechanical Engineering, National Chung Cheng University, 168, University Rd., Min-Hsiung, Chia-Yi, 621, Taiwan, R.O.C.
2 Corresponding author. Tel.: +886-5-2720411 (Ext: 33305); fax: +886-5-2720589. E-mail address: imedsl@ccu.edu.tw (D.S. Liu).
3 Department of Materials Science and Engineering, I-Shou University, No. 1, section 1, Shiuecheng Road, Dashu Shiang, Kaohsiung Country, Taiwan, 840, R.O.C.

Computers, Materials & Continua 2012, 28(2), 97-120. https://doi.org/10.3970/cmc.2012.028.097

Abstract

Manufacturing defects in the membrane of MEMS (Micro-Electro-Mechanical-Systems) structures have a significant effect on the sensitivity and working range of the device. Thus, in optimizing the design of MEMS devices, it is essential that the effects of membrane defects (e.g., cracks) can be predicted in advance. Accordingly, this study proposes the detailed two-dimensional Infinite Element Method (IEM) formulation with Infinite Element (IE)-Finite Element (FE) coupling scheme for analyzing the out-of-plane vibration of isotropic MEMS membranes containing one or more tip cracks. In the proposed approach, a degenerative computation scheme is used to condense the multiple element layers of the IEM domain to a single layer with master nodes at the boundary only. The validity of the proposed algorithm is demonstrated by comparing the results obtained for the vibration of a rectangular membrane with the analytical solutions and the solutions obtained using the conventional Finite Element (FE) method, respectively. The validated IEM algorithm is then coupled with an FE scheme to analyze various cracked membrane vibration problems. The results show that the fundamental frequency of the membrane changes in accordance with the membrane thickness, but is unaffected by the number of cracks. However, it is shown that a change in the location of the cracks may cause a shift or rotation of the wave peaks of the structural mode shape. In general, the IEM algorithm presented in this paper provides a fast modeling, direct, and accurate tool to simulate the effects of cracks on the dynamic response of MEMS membranes. Furthermore, the algorithm can be easily integrated with experimental methods in order to test for the presence of cracks as part of the MEMS membrane quality control process.

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