An improved model for the dynamic analysis of plates stiffened by parallel beams

In this paper a general solution for the dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric 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. These tractions are integrated with respect to each half of the interface width resulting 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 describing better in this way the actual response of the plate–beam system. 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. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. 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 plate–beam 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. Three additional finite element models using beam, shell or solid finite elements are also employed for the verification of the accuracy of the results of the proposed model.