FREE VIBRATIONS OF FREE-FREE WEB-STIFFENED SANDWICH BEAMS.

Presented herein is an analysis of the free vibrations of free-free, web-stiffened sandwich beams. The mathematical model formulated includes the effect of translatory and rotatory inertia in each layer of the sandwich, and assumes that the faces may be treated as thin layers in which classical beam theory applies. Shear deformations, however, are permitted in the core, which is treated as a layer of orthotropic material comprised of a series of webs considered as discrete elements, except for the inclusion of an average secondary shear modulus induced by the bending of the faces and the webs. Equations are also developed for the free vibrations of the corresponding homogeneously cored sandwich beams, in order to investigate the effect of smearing-out or averaging a given web-stiffened core. A Galerkin-type procedure is employed to determine the natural frequencies from a variational functional generated by means of Hamiltons principle. For free-free, web-stiffened sandwich beams of constant weight, the results show that smearing-out the web-stiffened core introduces significant error into the natural frequencies only when the mass in the core layer is distributed among a small number of webs. Author