以無網格局部Petrov-Galerkin法模擬電容式微麥克風在黏熱空氣中之問題

ANALYSIS OF COUPLING PROBLEMS IN THE MEMBRANE OF CAPACITIVE MICROMACHINED MICROPHONE IN VISCOTHERMAL AIR USING MESHLESS LOCAL PETROV-GALERKIN METHOD

於微機電電容式麥克風設計領域中，模擬麥克風振膜於空氣中之行為對於麥克風是否能達到高靈敏度及高良率極為重要，故模擬麥克風振膜之行為為本論文之主軸。MLPG（無網格局部Petrov-Galerkin法）為純無網格法，不同於傳統有限元素法（FEM）及邊界元素法（BEM），MLPG具場域變數內插或背景積分不需以網格處理之優點，故引進本研究探討微機電麥克風振膜於空氣中之行為。本文模擬1 mm半徑及10 μm厚之固定邊界軸對稱振膜在1 mm厚之黏熱空氣之行為，並與理論結果比較，最後模擬180 μm半徑及10 μm厚之固定邊界軸對稱振膜在10 μm厚之黏熱空氣之特性曲線，證明MLPG適合模擬振膜半徑大及薄黏熱空氣層之微機電麥克風。 The simulation of coupled problem of the microphone membrane in viscothermal air determines whether highest yieldand sentivity is attainable when it comes to the field of microelectromechanical system (MEMS) capacitive microphonedesign. MLPG, the meshless local Petrov-Galerkin method is introduced to differentiate from traditional finite elementmethod (FEM) and boundary element method (BEM) since MLPG model is truly messless and requires no mesh ofelements for both field variable interpolation and background integration. The result from a numerical axisymmetry modelof 1 mm radius and 10 μm thickness membrane with fixed boundary condition upon 1 mm thickness viscothermal air isidentical to that from the theoretical model. Finally, a MEMS axisymmetry model of a 180 μm radius and 10 μm thicknessmembrane upon 10 μm thickness viscothermal air is simulated in this paper.