一种新的非线性振动物理模型

A New Physical Model of Nonlinear Vibration

为建立合理反映损伤的混凝土结构振动控制方程,考虑损伤结构引起的拍振现象,引入弹簧线圈和阻尼线圈,分别串联组成复刚度弹簧和复阻尼器,建立一种新的非线性振动物理模型,通过构建等效刚度和等效阻尼,给出一般化振动方程的数学模型和关键参数的物理意义解释。最后通过对单自由度自由振动的能量分析,建立结构损伤与控制方程关键参数的单调变化关系,为寻找反映结构非线性损伤变化的识别指标提供了另一种思路。

In order to establish a governing equation of motion to rationally describe the phenomenon of beats in the vibration of a damaged concrete structure,a new nonlinear physical model is constructed by introducing a spring coil and a damping coil into a single degree of freedom system.In the model,the spring coil is connected in series with the spring of the system constituting a spring with complex stiffness,and the damping coil is connected in series with the damper of the system constituting a damper with complex damping.By introducing both the equivalent stiffness and damping,a generized governing equation of motion of the model and the physical explaination of its key parameters are obtained.By energy analysis of the free vibration of the system,a monotonic variation relationship between structural damage and the key parameters of the governing equation is created,which would probably afford a new idea of finding out an index used to identify the nonlinear damage of structures.