The Dynamics of Box Beams

Abstract

Box beams bend essentially with top and bottom skins providing bending rigidity and shear webs giving shear flexibility. When the width of the beam is comparable to the length of the beam and considerably larger than the depth ofthe shearwebs, there is an added complication called the shear lag effect. The free bending vibrations of box beams can be determined analytically by incorporating shear web assumption seleclively into the Timoshenko equations so thal areas active in inertia, bending deformation and shear deformation are carefully identified. This will accountfor both shearflexibility and rotary inertia,foctors that are omitted in classical Euler- Bernoulli beam descriptions. Frequencies from these modified Timoshenko type equations qre calculated for three types of end conditions namely simply supported, clamped-free and clamped-clamped. However, no single analytical treatment is possible to accountfor the shear lag effects in the cover sheets of the box beam. Here, thefinite element method allows a computational treatment of the problem. Frequencies are therefore obtained from finite element models of wing type box beam structures. The finite element models can now include the shear lag effects, which are not sensed by the Timoshenla beam model. Comparisons show how the box beam model can serve as a bench markfor evaluatingJinite element dynamic modeling and the relativeinfluences ofshear lagand shearflexibility coupled with rotatorv inertia can be identified.