Dynamic analysis of two flexible beams with repeated impact

Abstract

This paper analyzes the repetitive vibro-impact behavior of two flexible beams subjected to harmonic excitation. In order to analyze the vibro-impact behavior of two beams, a dynamic model of two flexible beams that can simultaneously collide at an arbitrary position is proposed. The impact mechanism of two flexible beams was considered by using the penalty method, one of the methods for modeling the impact phenomenon, and based on this, the equations of motion for the proposed model were derived. After discretizing the derived equations of motion by the finite element method, a numerical computation was performed to calculate the dynamic responses by using the generalize- time integration method. To obtain the dynamic responses of the two flexible beams with impact, the contact forces calculated every moment at the impact positions were applied to the discrete equations of motion. To verify the dynamic response of two beams obtained by the numerical computat-ion, an experimental setup was constructed, and the dynamic responses of two adjacent beams obtained from the dynamic model were compared with the dynamic responses obtained by the experiment. After the impact responses were verified, the vibro-impact behavior according to the change in material properties and size of the two beams was investigated, and the effect of the impact on the dynamic responses of the two beams was analyzed. In addition, the change of contact force and total energy caused by impact was further studied. Furthermore, the impact position, the number of impact, and the presence or absence of impact according to the change of the excitation frequency were investigated, and the correlation between the probability of occurrence of impact and the ratio of the natural frequency and the excitation frequency was also analyzed. Based on this analysis, a design guide that minimizes the probability of the impact when two adjacent beams are subjected to harmonic excitation is presented.