Influence of the Inplane Boundary Conditions on the Vibration Frequencies and Buckling Load of Ribbed Plates

In this paper, the influence of the inplane boundary conditions on the vibration frequencies and the buckling load of plates reinforced with a system of parallel beams is presented. The adopted model for the dynamic analysis of the ribbed plate takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The analysis of the vibration problem of a ribbed plate subjected to inplane forces is based on the capability to establish a flexibility matrix with respect to a set of nodal mass points using the Analog Equation Method (AEM) for the static ribbed plate problem. Moreover, a lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. The buckling load is established using the dynamic criterion. From the obtained results it is shown that both the vibration frequencies and the buckling load may be significantly influenced by the inplane boundary conditions.