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¯exibility 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.

Flexural-torsional Vibrations of Beams by BEM

“…Equations (1), (2) and (3) are solved using the Analog equation method as it is developed for hyperbolic differential equations [11,14]. This method is applied for the problem at hand as follows.…”

“…Following the numerical procedure analytically described in [11,14] and employing the constant element assumption, the discretized integral form of the solution of Eq. (16) and their derivatives at the N collocation points is…”

Building floor analysis by the boundary element method

“…The works published by Song [7] and Hartmann & Zotemantel [8] have shown interesting BEM approaches to deal with building frame floors, where displacement restrictions at internal points and the use of hermitian interpolations are discussed in details. More recently, several other woks appeared improving the BEM based numerical model to deal with this kind of structures [9][10][11][12][13][14]. For all these works, coupling BEM with FEM was the natural choice to develop the numerical scheme.…”

A BEM formulation for analysing the coupled stretching–bending problem of plates reinforced by rectangular beams with columns defined in the domain

“…In [13][14][15][16] are proposed BEM formulations for analysing the bending problem of beam-stiffened elastic plates. An alternative scheme to deal with zoned domains without dividing them into sub-regions has been proposed by Venturini [17,18].…”