在气垫导轨上进行橡皮筋滑块系统的自由振动实验，测量了系统的振动周期和对数减缩。理论分析与实验值相差甚远，说明不能将橡皮筋滑块系统的自由振动按谐振子的粘性阻尼振动处理。提出含分数阶导数振子自由振动模型，采用数值方法和平均法求解含分数阶导数项的二阶常微分方程，发现此模型理论分析结果与实验情况相符，说明采用弹性系数、粘弹度和粘弹系数描述橡皮筋力学性质是可行的。
Abstract
Free vibration tests of rubber band slider system was conducted on air cushion track to measure the system’s vibration period and logarithmic decrement. The large difference between theoretical analysis and test results showed that the free vibration of rubber band slider system can’t be treated as viscous damping vibration of a harmonic oscillator. Then, a free vibration model of oscillator containing fractional derivative was proposed. The second order ordinary differential equation with fractional derivative term was solved using the numerical method and the average one. It was found that the theoretical analysis results of this model are consistent with the test ones to reveal it is feasible to describe mechanical properties of rubber band using elastic coefficient, viscoelasticity and viscoelastic coefficient.
关键词
橡皮筋 /
分数阶导数 /
自由振动 /
平均法 /
粘弹性
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Key words
rubber band /
fractional derivative /
free vibration /
average method /
viscoelasticity
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