摘要
离散系统的振动理论中,主频率和主振型是表征该系统的固有性质;在数学上,可以归结为求振动系统的广义特征值问题。对于同一个振动系统,系统的运动微分方程可以选取不同形式。系统的主频率或特征值是一标量,不随系统的变换而改变,而系统的主振型或特征矢量,其正交性及表达形式随系统的变换而改变。本文试图以两个自由度系统的均质刚梁为例进行讨论。
Nature of the vibration of the discrete system is discussed with the principal frequencies and the principal modes. In the mathematics, they are both the generalized eigenvalue problems.For a discrete vibration system, the differential equations of motion are written with several kinds of forms. The principal frequency is an arthmetic quantity. It does not vary with the transformation of system. But the principal mode is a vector, it varies with the transformation of system.The Orthogonality and form of the principal modes are changed by the transformation of system.In this paper, we illustrate the discussion with vibration of a uniform rigid beam.
