DYNAMIC ANALYSIS OF SHALLOW SHELLS OF RECTANGULAR BASE

Abstract

In this investigation a systematic analytical procedure for the dynamic analysis and response of thin shallow shells with a rectangular layout is presented. The shell types examined are the elliptic and hyperbolic paraboloid, the hypar, the conoidal parabolic and the soap-bubble shell, although in principle any shell geometry expressed by a continuous surface equation can be treated. The eigenvalue problem solution is based on the one hand on the consideration of the shell as a system of two interdependent plates whose boundary conditions comply with the prevailing bending and membrane boundary conditions of the shell, and on the other hand on the consistent use of beam eigenfunctions, in the context of a Galerkin solution procedure. The series solution obtained in this way converges rapidly and provides practically acceptable results even in cases with one or more free edges, where the boundary conditions cannot be strictly satisfied. The whole analysis is carried out on the basis of a few non-dimensionalized geometrical parameters, which are the only input required for the computer program specially written for that purpose.