Vibro-impact analysis of two adjacent cantilever beams

Abstract

This study analyzes the vibro-impact behavior of two adjacent cantilever beams subjected to vibration generated by applying harmonic excitation to their rigid base. For the investigation, a dynamic model of two flexible beams that can collide at arbitrary positions along the beam length is proposed. The vibro-impact mechanism of the two flexible beams was considered using the penalty method, and the equations of motion for the proposed model were derived. After discretizing the derived equations of motion using the finite element method, a numerical analysis was implemented to calculate the dynamic responses using the generalized-alpha time integration method. The contact force due to the impact between the two beams was calculated by applying the well-known penalty method. The calculated contact forces at the impact positions were applied to the discretized equations of motion for response computations. To verify the results, the dynamic responses derived by numerical analysis were compared with the experimentally measured responses. Using the numerical analysis of the proposed dynamics model, the effect of vibro-impact on the dynamic responses was evaluated. Moreover, the relationship between the probability of vibro-impact occurrence and ratio of natural frequency to excitation frequency was examined. Based on the evaluation, a design guide that minimizes the probability of vibro-impact when two adjacent beams are subjected to vibration generated by applying harmonic excitation to their rigid base is presented.