On the limits of quasi-static analysis for a simple Coulomb frictional oscillator in response to harmonic loads
On the limits of quasi-static analysis for a simple Coulomb frictional oscillator in response to harmonic loads
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DOI：
10.1016/j.jsv.2014.11.028
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发表时间：
2015-03
影响因子：
4.7
通讯作者：
A. Papangelo;M. Ciavarella
中科院分区：
文献类型：
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作者：
A. Papangelo;M. Ciavarella
由于库仑摩擦定律的非线性，即使是最简单的接触界面模型也显示出非常丰富的动态解。特别是当加载频率仅为系统第一固有频率的一小部分时，通常需要用准静态分析代替完整的动态分析，这显然更容易获得。本文研究了简谐切向载荷作用下的库仑摩擦振子。据发现，准静态的解决方案（只有2个停止）捕获近似的位移峰值，只要迫使频率是足够低的动态解决方案有2个，甚至更好，超过2个停止。相反，速度峰值没有被正确地估计，因为速度由于粘滑停止而变得高度不规则，粘滑停止的数量对于零频率无限制地增加。在这个意义上，经典的准静态解，通过取消惯性项的平衡方程，不符合在低频率的全动态解决方案的限制。通过增加少量的粘性阻尼不能消除这种差异，因为只有在临界阻尼的情况下，动态解才非常接近准静态解。在极限频率以上会出现额外的差异，其值取决于切向载荷与滑动极限载荷之比，并且对应于动态解在每个周期从2停止变为0停止时。
Due to the nonlinearity of the Coulomb friction law, even the simplest models of interfaces in contact show a very rich dynamic solution. It is often desirable, especially if the frequency of loading is only a fraction of the first natural frequency of the system, to replace a full dynamic analysis with a quasi-static one, which obviously is much simpler to obtain. In this work, we study a simple Coulomb frictional oscillator with harmonic tangential load, but with constant normal load. It is found that the quasi-static solution (which has only 2 stops) captures approximately the displacement peak as long as the forcing frequency is low enough for the dynamic solution to have 2 or, even better, more than 2 stops. Instead, the velocity peak is not correctly estimated, since the velocity becomes highly irregular due to the stick–slip stops, whose number increases without limit for zero frequency. In this sense, the classical quasi-static solution, obtaining by cancelling inertia terms in the equilibrium equations, does not coincide with the limit of the full dynamic solution at low frequencies. The difference is not eliminated by adding a small amount of viscous damping, as only with critical damping, the dynamic solution is very close to the quasi-static one. Additional discrepancies arise above a limit frequency whose value depends on the ratio of the tangential load to the limit one for sliding, and correspond to when the dynamic solution turns from 2 to 0 stop per cycle.