Dynamic analysis of thin-walled members using Generalised Beam Theory (GBT)

• GBT formulation for the dynamic analysis of thin-walled members.
• Original “doubly modal” representation of the member response.
• Ability to isolate contributions from deformation modes or vibration modes to the member response.
• Illustrative examples: lipped channel beam under time-varying or moving loads.
• GBT-based results validated through comparison with shell finite element or analytical values.

This paper presents the main steps and procedures involved in the development of a Generalised Beam Theory (GBT) formulation to perform dynamic analyses of thin-walled members subjected to initial perturbations or acting loads. It combines (i) the GBT modal discretisation of the cross-section deformation with (ii) the commonly adopted vibration mode superposition approach – this combination leads to an original “doubly modal” representation of the displacement field, which (i) provides deep insight into the mechanics involved in the dynamic response under consideration and, moreover, (ii) makes it possible to obtain accurate results with surprisingly low degree of freedom numbers. The application and potential of the formulation is illustrated by presenting and discussing numerical results concerning the dynamic responses of cold-formed steel lipped channel beam in several situations, namely (i) the damped oscillations following the release from a deformed configuration, (ii) the action of uniformly distributed loads with periodic (sinusoidal and square-wave) and impulsive (rectangular) time variations, and (iii) the effect of a point load moving along the span with constant speed. For validation purposes, the GBT-based results are compared with values yielded by Ansys shell finite element analyses – the total number of degrees of freedom involved in the GBT analyses was significantly lower.