1D-Hierarchical Ritz and 2D-GDQ Formulations for the free vibration analysis of circular/elliptical cylindrical shells and beam structures

Abstract

The present paper proposes a comparison between two different computational techniques to evaluate the natural frequencies of some selected structural components. More specifically, three case studies are investigated: i) Isotropic circular and elliptical cylindrical shells; ii) Non-homogeneous circular cylindrical shell sectors; iii) Homogeneous and non-homogeneous rectangular beams. The 1D-Hierarchical Ritz Formulation (HRF) with 3D capabilities and the 2D-Generalized Differential Quadrature (GDQ) formulation (both in a weak- and a strong-form) are assessed by using a Finite Element Method (FEM) software. For both computational methodologies the Method of Power Series Expansion of the Displacement Components (MPSEDCs) has been employed. A parametric investigation is performed to study the sensitivity of the natural frequencies to some significant parameters, namely, the boundary conditions, the length-to-thickness ratio, as well as some material and geometrical properties. The main advantages of the proposed solution techniques are discussed in terms of convergence and accuracy, for each selected case study.