Generalized Beam Theory to Analyze the Vibration of Open-Section Thin-Walled Composite Members

Abstract

This paper presents the formulation of a generalized beam theory (GBT) to analyze the vibration behavior of composite thin-walled prismatic members displaying straight axis, open-section, and arbitrary orthotropy. It accounts for the effects of (1) the cross section in-plane deformation, (2) geometric and material couplings, (3) primary and secondary warping, and (4) rotary inertia. First, the GBT equilibrium equations and boundary conditions are derived, and their terms are physically interpreted, i.e., related to the member mechanical properties. Then, a few remarks on the cross-section mechanical properties appearing in the linear stiffness and inertia terms are presented. Finally, to clarify the concepts involved in the proposed GBT formulation and illustrate its application and capabilities, an in-depth study concerning the local and global vibration behavior of lipped channel members with (1) simply supported end sections and wall cross-ply orthotropy and (2) fixed (clamped) end sections and wall nonaligned orthotropy are presented and discussed in detail.