Multiple Impacts in Rigid Bodies

Abstract:
Multiple impacts problems arise in many practical applications, such as airplane undercarriages, impact crushers, and assembly robots. Solution of rigid body impact problems that involve simultaneous collisions is a challenging problem in mechanics and dynamics. This is one of the classical problems of contact mechanics, an area that dates back to Galileo. Surprisingly, the few methods that produced energetically consistent, unique solutions to this class of problems were proposed in the last decade. Among these methods, only the Impulse Momentum based method has been thoroughly verified by experiments. This method depends on a parameter called the Impulse Correlation Ratio (ICR). This parameter is physically meaningful and more effective in dealing with multiple impact problems. In this paper, we present a solution to the frictionless multiple impact problems that may arise in the rocking blocks. We use an approach based on the Impulse Momentum based method, the energetic coefficient of restitution, and the Impulse Correlation Ratio (ICR). Subsequently, we present the results of an experimental study that is used to compare the results predicted by the proposed method with the experimental outcomes.