Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

Abstract

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at postcritical speeds, and divergence instability takes place precritical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented.

Transverse Vibrations and Stability of Axially Traveling Sandwich Beam With Soft Core

“…They found the natural frequency on the longitudinal direction is much higher than that of the transverse direction, which ensures the validity of the beam model. Gaith and Müftü [25] used the double beam model interconnected by a Winkler foundation to study the dynamics of axially moving laminated materials. In 2005, Yang et al [26] first performed an investigation on the vibrations of a traveling sandwich beam by the finite element method.…”