Dynamic Response of Clamped Beams Impulsed by a Spherical Steel Impactor. A Comparison between Numerical and Experimental Results.

Abstract

A few studies have been reported on the transient vibration of clamped beams impulsed by a spherical impactor. The governing equation of the transient vibration becomes a nonlinear equation due to the contact force between the beam and impactor, and due to the axial force caused by bending of the beam. Although effects of contact force and axial force on the transient vibration of the beam have been studied independently in some reports, one can find no reports discussing both effects. In the present study, it is assumed that the contact force can be estimated by the Hertzian force-deformation relationship. A numerical approach has been proposed for taking into account effects of both contact force and axial force. With the comparison of numerical results and experimental ones, it follows that one can estimate accurately the deflection of the beam and the axial force caused by bending using the proposed approach. From numerical results, furthermore, it has been made clear that one cannot neglect the effect of the axial force caused by bending on the deflection in the case of the clamped thin beam.