Dynamic analysis of elastic plates reinforced with beams of doubly-symmetrical cross section

Abstract

In this paper a solution to the dynamic problem of elastic plates reinforced with beams of doubly – symmetrical cross section is presented. The adopted model 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 method of analysis 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 plate problem. A lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. Both free and forced 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-beams system, and the corresponding ones ignoring the inplane forces and deformations justify the analysis based on the proposed model.