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推导建立了一个用于微电子机械 (MEMS)器件压膜空气阻尼的一般化微分方程 .该方程很好地解决了分析有限尺寸孔板的边界和孔板的厚度对压膜阻尼的影响的困难 .结合边界条件求解该方程可以得到各种压膜阻尼结构中的阻尼压强分布和阻尼力 .以长条板为例得到了有限宽度和有限厚度孔板压膜阻尼的压强分布和阻尼力的解析解 ,在非孔板的条件下该解退化为一般传统雷诺方程的解 ,而在无限大薄孔板的极端条件下 ,该解也与传统雷诺方程在此条件下的解相一致 ,进一步证明了该方程的正确性 .因此 ,该一般化的雷诺方程为 MEMS器件的压膜阻尼设计提供了有效的手段
A generalized differential equation for air damping of dielectrics of microelectromechanical (MEMS) devices is deduced.The equation is a good solution to the difficulty of analyzing the influence of the boundary of finite-size plate and the thickness of orifice on the film damping The damping pressure distribution and the damping force of various diaphragm damping structures can be obtained by solving this equation with the boundary conditions.The pressure distribution and damping force of the diaphragm with finite width and limited thickness are obtained by taking the long slab as an example Solution, this solution degenerates into the solution of the general traditional Reynolds equation under non-orifice conditions, which is also consistent with the solution of the traditional Reynolds equation in this condition under the extreme conditions of an infinitely large thin-walled plate The correctness of this equation.Thus, the generalized Reynolds equation provides an effective means for the design of film damping for MEMS devices