一种分析微悬臂梁大挠度变形的新算法

考虑静电力边缘效应的影响,建立了微悬臂梁大挠度变形的静态变形分析模型,通过梁弯曲理论将控制方程化为一阶非线性微分方程组,结合非线性方程组求根、迭代修正齐次扩容精细积分法和增量迭代法,提出了一种分析微悬臂梁大挠度变形的半解析、半数值算法。数值算例表明:该方法具有较高的精度和稳定性,是分析微悬臂梁变形的一种有效方法;通过对微梁静态特性的分析表明:考虑边缘效应后微梁的吸合电压减小,考虑大挠度变形的影响后微梁的吸合电压增加。

Novel method for analyzing large deflection deformation of micro-cantilevers

Considering the influence of electrostatic force edge effect,a model is established to analyze the static deformation of a micro-cantilever with large deflection,and the control equations are changed to first order nonlinear differential equations about the beam bending theory.A semi-analytical semi-numerical method is presented for analyzing micro-cantilever deformation by means of the high precision iterative refinement extended homogeneous capacity integration method,nonlinear equations solution and incremental iterative algorithm.Numerical calculated results show that the method has upper precision and stability,which is an effective method to analyze the deformation of a micro-cantilever.Static characteristics show that the pull-in voltage decreases when edge effects are considered,and the pull-in voltage increases when the influence of large deflection is considered.