Consider The Damping Effect Of The Double Flexible Rod Repeated Impact

The impacts phenomena of rod-like structure are of wide significance in the field ofengineering, especially the repeated impacts between some flexible structures can causesome unexpected problems, such as vibrations, wears, impact noises and failures etc. Theinfluence of the repeated impacts between flexible structures on the dynamic behaviors ofthe system need to be investigated deeply and fully due to that the high-precision and highvelocity mechanism is expected.The phenomenon of repeated longitudinal impacts between two flexible rodsconsidering damping effect has been investigated in the present paper. The transient wavepropagation based on St.Venant's rod theory was presented and the problem of repeatedimpacts was solved by the expansion of transient wave functions in a series ofeigenfunctions. The effects of the transient wave propagation induced by impacts anddamping effect were fully considered during the phases of impact and separation correctly.The new method of solving the impact force was presented that avoided to solve theimpact force from the strongly nonlinear equation coupled of impact force with impactmotions. Further, the effects of initial impact velocity and air damping coefficient on theimpact force and transient responses were investigated in detail. The numerical resultsshown that the present method can simulate the processes of multiple impacts and thetransient wave propagations successfully.Some useful conclusions can be obtained based on the analytical and numericalresults:1. The analytical solutions of the repeated impacts between two flexible rodsconsidering the damping effect have been introduced reasonably.2. The numerical results showed that the damping effect is not remarkable duringinitial stages of repeated impacts, so it can be neglected.3. After some impacts phases took place, the damping effect worked gradually. Ithas an outstanding influence on the system response with the number of therepeated impacts increasing. The damping effect not only influenced the forceresponses, the displacement and velocity responses of structures, but also hadinfluence on the time when the impact phases or the separation phases happened.Therefore, the essential characteristic will be changed.