Global–Local-Distortional Vibration of Thin-Walled Rectangular Multi-Cell Beams

Abstract

This paper presents the results of an investigation concerning the free vibration behavior (undamped natural frequencies and vibration mode shapes) of thin-walled beams with rectangular multi-cell cross-section (assemblies of parallel rectangular cells in a single direction). Besides local (plate-type) and global (flexural, torsional and extensional) vibration modes, attention is paid to the relatively less-known distortional vibration modes, which involve cross-section out-of-plane (warping) and in-plane deformation, including displacements of the wall intersections. A computationally efficient semi-analytical Generalized Beam Theory (GBT) approach is employed to obtain insight into the mechanics of the problem. In particular, the intrinsic modal decomposition features of GBT — the fact that the beam is described using a hierarchical set of relevant cross-section deformation modes — are exploited to identify and categorize the most relevant vibration modes and deformation mode couplings.