Shear deformation effect in the dynamic analysis of plates stiffened by parallel beams

In this paper a general solution for the dynamic analysis of shear-deformable stiffened plates subjected to arbitrary loading is presented. According to the proposed model, the arbitrarily placed parallel 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. These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account the second-order effects. The analysis of the plate is based on Reissner's theory, which may be considered as the standard thick plate theory with which all others are compared, while the analysis of the beams is performed employing the linearized second-order theory taking into account the shear deformation effect. 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. Six boundary value problems are formulated and solved using the analog equation method, a BEM-based method. Both free and forced damped or undamped transverse vibrations are considered and numerical examples with great practical interest are presented demonstrating the effectiveness, the range of applications of the proposed method and the influence of the shear deformation effect.