Batra Romesh C, Porfiri Maurizio, Spinello Davide
Department of Engineering Science & Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA.
Department of Mechanical & Aerospace Engineering, Polytechnic University, Brooklyn, NY 11201, USA.
Sensors (Basel). 2008 Feb 15;8(2):1048-1069. doi: 10.3390/s8021048.
We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically, we reduce the governing two-dimensional nonlineartransient boundary-value problem to a single nonlinear ordinary differential equation. For thestatic problem, the pull-in voltage and the pull-in displacement are determined by solving apair of nonlinear algebraic equations. The fundamental vibration frequency corresponding toa deflected configuration of the microplate is determined by solving a linear algebraic equa-tion. The proposed reduced-order model allows for accurately estimating the combined effectsof van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflectionprofile with an extremely limited computational effort.
我们研究了冯·卡门非线性、范德华力和非热应力对静电驱动微板的拉入不稳定性和小振动的影响。我们使用伽辽金方法来建立一个易于处理的降阶模型，用于存在范德华力和热应力的静电驱动夹紧矩形微板。更具体地说，我们将控制二维非线性瞬态边值问题简化为一个单一的非线性常微分方程。对于静态问题，通过求解一对非线性代数方程来确定拉入电压和拉入位移。通过求解一个线性代数方程来确定与微板挠曲配置相对应的基频振动频率。所提出的降阶模型能够以极少的计算量准确估计范德华力和热应力对拉入电压和拉入挠度分布的综合影响。
