Trajectory Piecewise-linear Model Order Reduction Technique for Nonlinear Bistable Mechanism
Date Issued
2007
Date
2007
Author(s)
Huang, Ying-Yin
DOI
zh-TW
Abstract
In this work, we investigate the applications of the trajectory piecewise-linear model order reduction (TPWLMOR) technique on bistable mechanisms. The bistable mechanism, which is composed of a double curved-beam mechanism (DCBM), is employed in an MEMS (micro-electro-mechanical systems) optical switch. While applying an external force which is larger than a certain critical value, the DCBM quickly snaps through from a stable state to another stable state. We focused on analyzing the properties of the static and transient behaviors of the DCBM.
First, we used the finite element method (FEM) software, ABAQUS, to construct a 3-D solid model of the DCBM and to simulate both the static and the transient analyses. Subsequently, we developed a 3-D dynamic nonlinear FEM numerical model. Then, the TPWLMOR is used to reduce the full-mesh FEM models into low-order models. The idea of TPWLMOR comes from the concept of piecewise-linear approximation and an Arnoldi-based model order reduction (MOR) algorithm. Reduced models are generated using the Arnoldi algorithm at appropriate linearization points, and then are superposed into a compact model (i.e., the trajectory piecewise-linear model) using weighted sum. Compared to traditional FEM modeling, the TPWLMOR models increases computational efficiency.
The bistable device was realized using a simple SOI MEMS process with one photo-mask. Then we set up a Doppler laser interferometer system in order to measure the dynamics of the DCBM. We then compared the empirical data with the simulated dataset obtained by ABAQUS , FEM, and the TPWLMOR algorithm. The simulated DCBM displacements of the reduced models agree with the results of the ABAQUS, while the computational performance reaches 200 times of that of the ABAQUS. However, when the force is larger than the critical value, the DCBM does not snap-through as expected. The inaccurate results might be caused by many factors, which are subject to further study.
Subjects
雙穩態
非線性
跳躍
有限元素法
片段線性
降階法
微機電
bistable
nonlinear
snap-through
finite element method (FEM)
trajectory piecewise linear (TPL)
model order reduction (MOR)
micro-electro-mechanical systems (MEMS)
Type
thesis
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