Dynamic Analysis Of Plates Stiffened By Parallel Beams
Free (open access)
E. J. Sapountzakis & V. G. Mokos
In this paper a general solution for the dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary cross section subjected to an arbitrary dynamic loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. The aforementioned integrated tractions result in the loading of the beams as well as the additional loading of the plate. Their distribution is established by applying continuity conditions in all directions at the interfaces. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The method of analysis is based on the capability to establish a flexibility matrix with respect to a set of nodal mass points, while a lumped mass matrix is constructed from the tributary mass areas to these mass points. Both free and forced damped or undamped transverse vibrations are considered and numerical examples with great practical interest are presented. The discrepancy in the obtained eigenfrequencies using the presented analysis (which approximates better the actual response of the platebeams system since it permits the evaluation of the shear forces at the interfaces in both directions) and the corresponding ones ignoring the inplane forces and deformations justify the analysis based on the proposed model. Keywords: reinforced plate with beams, nonuniform torsion, warping, ribbed plate, slab-and-beam structure, vibrations, dynamic analysis.
reinforced plate with beams, nonuniform torsion, warping, ribbed plate, slab-and-beam structure, vibrations, dynamic analysis.