非线性MEMS微梁的重心有理插值迭代配点法分析  

NONLINEAR MEMS MICROBEAM ANALYSIS BY BARYCENTRIC RATIONAL INTERPOLATION ITERATION COLLOCATION METHOD

作　　者：王兆清[1] 庄美玲[1] 姜剑[1] 

机构地区：[1]山东建筑大学力学研究所,济南250101

出　　处：《固体力学学报》2015年第5期453-459,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51379113)资助

摘　　要：通过假设初始函数,将微梁非线性控制方程转换为线性化微分方程,建立逼近非线性微分方程的线性化迭代格式.采用重心有理插值配点法求解线性化微分方程,提出了数值分析MEMS微梁非线性弯曲问题的重心插值迭代配点法.给出了非线性微分方程的直接线性化和Newton线性化计算公式,详细讨论了非线性积分项的计算方法和公式.利用重心有理插值微分矩阵,建立了矩阵-向量化的重心插值迭代配点法的计算公式.数值算例结果表明,重心插值迭代配点法求解微梁非线性弯曲问题,具有计算公式简单、程序实施方便和计算精度高的特点.The nonlinear governing equation of micro beams is transfered into the linear differential equation by assuming the initial function.Barycentric rational interpolation collocation method is applied to solve linear differential equation.The direct linearization formulations and the Newton linearization formulations of nonlinear differential equation are given.The calculation method and formulation of nonlinear integral item are discussed in detail.The matrix-vector calculation formula of barycentric rational interpolation iteration collocation method is constructed by using barycentric rational interpolation differentiation matrix.Numerical examples demonstrate that the presented method for solving nonlinear bending problem of MEMS micro beams has several merits of simple calculation formulations,convenient program and high calculation precision.

关 键 词：非线性微梁 重心有理插值 配点法 线性化方法 迭代法 

分 类 号：O302[理学—力学]