中文摘要：

应用二阶中心差分公式，建立了任意支承的Euler梁的差分离散系统，导出了与之等效的弹簧，质点-刚杆模型．利用振荡矩阵理论，证明了上述系统的刚度矩阵的符号振荡性，完整的导出了正系统的充分必要条件。

英文摘要：

The difference discrete system of Euler beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass pointrigid rod model. By using the theory about oscillatory matrix, the sign-oscillatory property of stiffiness matrices of this system was proved, and necessary and suffident condition for the system to be positive is obtained completely.