Computational Model for Vibration and Buckling of Thin and Thick Annular Plates

Joaquín Leonel Sánchez Salas¹; Raul Rosas e Silva¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/COB-2015-1883

Resumo

This paper uses a version of the Rayleigh-Ritz method with specialized functions for the analysis of thin and thick circular and annular plates subjected to out-of-plane and in-plane loads. The approximation functions for displacements are polynomials in the radial direction combined with trigonometric functions in the circumferential direction. A convenient feature is the use of linear nodal functions, which allow for easy consideration of nodal loads and boundary conditions (including follower forces), enriched by higher order polynomials without inclusion of additional nodes. The model allows for thickness variation and was implemented in MAPLE18, enabling the calculation of displacements and stresses under constant and linearly varying load, frequencies of vibration and buckling loads with a few commands. The examples show the effectiveness of this approach in the analysis of such structures and bring new light to this classical problem, presenting interesting and novel comparisons illustrating the effect of shear deformation and thickness variation in circular and annular plates, including displacements, moments and shear forces, vibration frequencies and buckling loads.

Palavras-chave: Circular annular plate; variable thickness circular plates; natural frequencies; buckling of annular plates; Rayleigh-Ritz method