中文摘要：

微梁是微机电系统中的常见结构,尺寸效应是微梁不同于其他梁的重要特征.基于偶应力理论和最小势能原理,推导了微梁弯曲时一阶微分方程组和边界条件,通过引入状态向量,建立微梁状态向量间的传递关系,得到系统的状态空间方程,并借助精细积分法求解传递矩阵,建立了一种分析微梁尺寸效应的高精度传递矩阵法.数值结果验证了本文的有效性.

英文摘要：

The micro-beam is the common structure of MEMS（micro-electro-mechanical system）, of which the size effects are the significant characteristic different from other beams. The first order differential equations and boundary conditions of the micro-beam bending deformation are derived from the couple stress theory and the principal of minimum potential energy. The transfer relations between the state vectors are established, and the state space equations are obtained. Precise integration method is used to solve the transfer matrix. So the transfer matrix method with high precision is set up to analyze the size-dependent effects of micro-beam. Several numerical examples are used to test the present method and the results show the validity of the method.