Abstract: A simple method called Numerical-Axis-Method for establishing the mathematical models of the common mass-spring-damper systems was put forward. In establishing the mathematical model, a numerical-axis parallel to the system was built, and the displacements of the spring or the damper were translated to the rational numbers which were marked on the numerical-axis. Then the magnitude and the direction of spring force or damping force applied to the corresponding mass was determined by comparing the two rational numbers mutually. The application of this method on establishing the mathematical models of mechanical vibration systems was expatiated through a single degree-of-freedom (DOF) system, a double DOF system and a multi-DOF system. The results show that this method was very efficient in establishing the kinematic differential equations of the mass-spring-damper systems.

Key words: vibration and wave, mechanical vibration, mass-spring-damper system, mathematical model, numerical-axis, differential equations

摘要： 提出一种建立弹簧―质量―阻尼系统其数学模型的简单方法——数轴建模法，即建立与系统平行方向的数轴，把弹簧或阻尼器的实际位移值当做有理数标在数轴上对应位置，然后按照有理数比较大小的结果确定相应质量块所受弹簧力或阻尼力的大小和方向，进而求得系统的微分方程。分别以单自由度系统、两自由度振动系统及多自由度系统为例，阐述了数轴法在建立机械振动系统的数学模型中的应用。结果表明此方法在列写弹簧―质量―阻尼系统的运动微分方程时非常有效。

关键词: 振动与波, 机械振动, 弹簧－质量－阻尼系统, 数学模型, 数轴, 微分方程