The vibrations of isotropic, linear elastic, cylindrical, shallow and deep shells are analyzed using a p-version finite element. First order shear deformation theory is followed, i e, it is assumed that the transverse shear deformation is constant along the panel’s cross section. The element is a shallow shell one , but using several elements it becomes possible to analyze deep shells
In the applications, natural frequencies of shells with different curvatures are comuuted. The boundary conditions are: completely free, clamped on the straight boundaries and free on the curved ones, free on the straight and clamped on the curve boundaries. The values obtained are compared with published values or with values from an ABAQUS model and, in general, very good ageement is found. Two different sets of polynomial functions, named as f and g, are tried and they, eive the same results. with similar number of demes of freedom. It is shown that the p-version element employed allows one to define an accurate model with a moderate - and smaller than h-version elements -number of degees of freedom.
enrichment is very efficient, the geometry of the shell under study should be well a.n.n r oximated. Therefore. for deener shells. as for examnle shells where the projected length is 1.5 times the radius of curvature, it becomes necessary to use several elements, consequently increasing the number of degrees of freedom ofthep-version FEM model.
A preliminary analysis of forced vibrations of shallow and deep shells is carried out, using Newmark’s implicit numerical interntion scheme. The forces considered are harmonic in time. For low amplitude vibrations, the response is vev close to harmonic, irrespective of the shells curvature. With the help of Fourier Spectra and other plots, it is confmed that large amplitude vibrations lead to non-harmonic, in some cases multi-modal, response to harmonic excitations.