## Reduced-Order Modeling of Weakly Nonlinear MEMS Devices with Taylor-Series Expansion and Arnoldi Approach (2004)

Venue: | TRANSDUCERS MAGAZINE (S&T E-DIGEST) |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Chen04reduced-ordermodeling,

author = {Jinghong Chen and Sung-Mo (Steve) Kang and Jun Zou and Chang Liu and José E. Schutt-Ainé},

title = {Reduced-Order Modeling of Weakly Nonlinear MEMS Devices with Taylor-Series Expansion and Arnoldi Approach},

booktitle = {TRANSDUCERS MAGAZINE (S&T E-DIGEST)},

year = {2004},

pages = {526--533},

publisher = {}

}

### OpenURL

### Abstract

In this paper, we present a new technique by combining the Taylor series expansion with the Arnoldi method to automatically develop reduced-order models for coupled energy domain nonlinear microelectromechanical devices. An electrostatically actuated fixed-fixed beam structure with squeeze-film damping effect is examined to illustrate the model-order reduction method. Simulation results show that the reduced-order nonlinear models can accurately capture the device dynamic behavior over a much larger range of device deformation than the conventional linearized model. Compared with the fully meshed finite-difference method, the model reduction method provides accurate models using orders of magnitude less computation. The reduced MEMS device models are represented by a small number of differential and algebraic equations and thus can be conveniently inserted into a circuit simulator for fast and efficient system-level simulation.

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Citation Context ...order to illustrate our model reduction approach and make comparisons, we will briefly review this approach and then show its limitations. We will emphasize the Arnoldi method and its properties [36]–=-=[38]-=-. To build the reduced linear model, we first perform the Taylor series expansion of the beam governing nonlinear partial differential (1) and (2) about its equilibrium state. Specifically, let us def... |

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Citation Context ...ion. Following Hung et al. [24], the dynamic behavior of this coupled electromechanical fluidic system can be modeled with the Euler beam equation and the Reynold’s squeeze-film damping equation [31]–=-=[35]-=- as where is the distributed electrostatic force, is the mechanical load from the squeezed air, is the height of the beam above the substrate, and is the pressure distribution under the beam. Equation... |

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Citation Context ...ation in an accurate and computationally efficient manner. The reducedorder models for the fixed-fixed beam device are further inserted into a mixed-mode and analog multilevel circuit simulator iSIMS =-=[28]-=-, [42] for mixed circuit and MEMS system-level simulation. The beam device model requires the user to input to the simulator the device geometry and material parameters including length, width, thickn... |

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Citation Context ...cal behaviors by constructing low-order device models to match with the direct analysis. A common approach for doing this is based on parameterized lumped element representation for MEMS devices [12]–=-=[16]-=-. In this approach, geometrically parameterized lumped behavioral models have been developed for a small set of atomic elements such as anchors, beams, plates, and electrostatic gaps. Layouts of these... |

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Citation Context ...es low accuracy, particularly for MEMS structures with large deflection, due to its rigid body assumption and linear approximation. Recently, a parameterized lumped nonlinear beam model was developed =-=[17]-=-. The model captures the geometric nonlinearity caused by large axial stress and large deflection, thus provides better accuracy when compared with the parameterized lumped linear beam model. Another ... |

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Citation Context ...in the linear regime. However, when the beam deflection is large, the linearized model deviates from the device nonlinear model significantly. Reduced-order nonlinear models are required. In [26] and =-=[27]-=-, the Arnoldi method was extended to develop reduced order models for nonlinear systems. The method first linearizes the system around an equilibrium point, and then extracts a Krylov subspace for red... |

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