A beam formulation with 3D capabilities for the free vibration analysis of thin-walled metallic and composite structures. (January 2020) - Fazzolari, Fiorenzo A.
Abstract: The present article proposes an advanced Ritz formulation with 3D capabilities for the analysis of thin-walled metallic and composite beam structures. Various set of admissible functions such as: Legendre, Chebyshev and algebraic polynomials, as well as hybrid functions are employed. The investigation is carried out by using the method of power series expansion of displacement components based on 2D-Taylor polynomials. The governing equations (GEs) are derived in their weak form via Hamilton's Principle and are solved by using the Ritz method. Convergence and stability of both cross-section and admissible functions have been thoroughly analysed. The high level of accuracy of the proposed formulation has been comprehensively examined in three selected case studies: (i) slender beams with arbitrary boundary conditions, and both solid and thin-walled cross-sections; (ii) a fully-clamped three-layer non-homogenous circular cylindrical shell; (iii) a fully-clamped functionally graded material (FGM) box resting on two-parameter elastic foundation. Highlights: The 1D Ritz formulation with 3D capabilities showed an excellent convergence rate. Higher-order beam models are mandatory to accurately analyse thin-walled beams. Lower-order beam models are acceptable in the analysis of beams with solid cross-section. For shell-like structures shell modes are completely detected. A 3D description of the free vibrational behaviour of beams is provided.