论文标题
刚性球对弹性膜的影响
Impact of a rigid sphere onto an elastic membrane
论文作者
论文摘要
我们在理论上和实验上研究了刚性球对弹性膜的轴对称影响。我们从第一原理中得出了管理方程，并在接触过程中对球体和膜的耦合运动施加了天然运动学和几何约束。通过迭代方法解决了找到接触表面的自由边界问题，该接触表面是由碰撞法引起的。这导致了一个模型，该模型可产生球体轨迹的详细预测，膜的挠度以及接触过程中的压力分布。我们的模型预测通过我们的直接实验测量进行了验证。此外，我们确定了有关低冲击速度恢复系数的行为的新现象，单个反弹期间多次接触的可能性以及随后的弹跳中的能量恢复。从这个模型问题中获得的洞察力可以为开发预测模型的持续努力提供有关在多个工程应用中自然出现的预测模型的努力。
We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our model predictions are validated against our direct experimental measurements. Moreover, we identify new phenomena regarding the behaviour of the coefficient of restitution for low impact velocities, the possibility of multiple contacts during a single rebound, and energy recovery on subsequent bounces. Insight obtained from this model problem in contact mechanics can inform ongoing efforts towards the development of predictive models for contact problems that arise naturally in multiple engineering applications.
