Abstract    This paper deals with the effect of the intrinsic material length-scale parameter on the stability and natural frequency of a rectangular micro-plate for two different cases; fully clamped and fully simply supported. A variational formulation based on Hamilton’s principle and the modified couple stress theory is used to obtain the nonlinear governing equation of a micro-plate incorporating the stretching effect. In the static case, the nonlinear governing equation is solved using the step-by-step linearization method (SSLM) and in the dynamic case, is integrated using fourth-ordered Runge-Kutta method. The static and dynamic pull-in parameters, limiting the stability regions of capacitive MEMS devices, are calculated and compared to those obtained by the classical theory. The numerical results reveal that the intrinsic size dependence of materials is more significant for smaller thicknesses and in this case, the stretching effect can be neglected.

Keywords    Material length-scale parameter, Modified couple stress theory, Rectangular micro-plate, Stability

چکیده    این مقاله به بررسی اثرات پارامتر مقیاس طول ماده روی پایداری و فرکانس طبیعی میکروصفحه‌ی مستطیلی در دو حالت کاملا گیردار و کاملا با تکیه‌گاه ساده می‌پردازد. برای به‌دست آوردن معادله‌ی غیرخطی حاکم بر میکروصفحه با در نظرگیری اثرات کشیدگی بر پایه‌ی تئوری تنش کوپل پیراسته از اصل همیلتون استفاده می‌شود. معادله‌ی غیرخطی حاکم، در حالت استاتیکی با استفاده از روش خطی‌سازی گام به گام و در حالت دینامیکی با انتگرال‌گیری از روش رانگ-کوتای مرتبه‌ی چهار حل می‌گردد. پارامترهای pull-in استاتیکی و دینامیکی که محدودکننده‌ی حوزه‌های پایداری دستگاه‌های MEMS خازنی است محاسبه شده و با مقادیر به‌دست‌ آمده از تئوری کلاسیک مقایسه می‌گردد. نتایج عددی نشان می‌دهد که وابستگی مواد به اندازه‌ی ذاتی در ضخامت‌های کمتر چشمگیرتر بوده و در این حالت اثرات کشیدگی قابل چشم‌پوشی است.

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