Flexible Body Containing Friction Oblique Collision Of Hybrid Analysis Model Method

For the simpler classical Fillipov system and a pulse non-smooth dynamical systems which are merely acted by the effect of friction and the collinear impact, respectively, the traditional methods are generally ignored the deformation effect of flexible structures and collision processes due to the non-smooth characters of the friction and the collinear impact. In order to lower the difficulty of solving analysis, these methods usually were based on Newton or Poisson coefficient of restitution rigid model. To reasonably estimating the more complex mechanical behavior of oblique collision with friction, this paper presents a hybrid analysis model which considers normal contact compliance, tangential contact compliance and the flexibility of the overall structure. A bilinear contact model based on Stronge energy coefficient of restitution is used to account for the normal contact pressure-restitution process and the tangential friction effects of the local contact zone. A finite segment method which naturally takes into account the geometric nonlinearity is used to discrete displacement field of the flexible beam, then the piecewise continuous dynamical equations are derived. The switching criteria for the tangential stick-slip relative motion and the normal compression-recovery phase are given and using event-driven method to solve the kinetic equation. By the use of the present model, the transient responses of the flexible beam oblique collision with a fixed plane are calculated. By comparing with the experimental data and the results of the three-dimensional dynamic finite element method, the accuracy and feasibility of the hybrid model are validated. It is shown that this hybrid model can accurately describe the repeatedly switching of the flexible beam stick-slip motion and tangential contact force time history.The study also found that the energy coefficient of restitution has no effect on the peak of the contact forces, but a significant effect on the normal separation velocity, meanwhile a tiny effect on the tangential velocity. The peak value of the pure sliding contact force is significantly less than the peak value of stick contact force. After the system appears stick state, if considering the flexibility of the structure, the peak of the contact force will not increase when the friction coefficient increases. If without considering the flexibility of the structure, the peak of the contact force will significantly increases when the friction coefficient increases. This suggests the structural flexibility has an important influence on the dynamics of the system. In addition, because the degree of freedoms of system are small and do not require the calculation iteration, this method overcomes the disadvantage of the conventional finite element need dense mesh elements which lead to a low efficiency.