On the warping of the extreme ends of a beam under flexural oscillations

• DOI: 10.1016/j.jsv.2018.08.019
• Publication Date: 2018-08-16T14:27:00Z
• Authors: J.C. Torres-Guzmán; A. Díaz-de-Anda; J.A. Otero; A. Morales; L. Gutiérrez; G. Monsivais; J. Flores
• Keywords: Image warping; Oscillation (cell signaling)

Abstract In this paper, we explain why beyond a certain critical frequency the extreme ends of a beam under flexural oscillations remain sometimes plane and in other cases become warped. We have seen this to be the case when the flexural oscillations of a beam are studied experimentally. Using the plane stress elastodynamic theory as well as a more precise calculation based on a 3D finite element method, we show for the first time that when the transverse displacement has a derivative equal to zero near the beam extremes, the ends can indeed become warped. In addition it is shown, from an energetic point of view, that warped modes result from a constructive spatial interference of the two components of flexural oscillations while flat modes result from a destructive interference of these two components.