Soft-impact dynamics of deformable bodies

Systems constituted by impacting beam and rod of non negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an in nite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of nite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between beam and rod at their contact point, simulating deformability of impacting bodies in the interaction zones. A reliable and convenient method for determining impact forces is also presented. A sample of engineering interest (a beam impacting on a rod) is carried out where a exible beam impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod respectively by superimposition of a nite number of modal contributions. Numerical investigations are performed in order to examine the in uence of the rigidity of the contact spring and of the ratio between the rst natural frequencies of the beam and the rod respectively on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non structural element is at risk.