Free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams

Article type: Research Article

Authors: Shahba, Ahmad^; | Attarnejad, Reza^; | Hajilar, Shahin

Affiliations: School of Civil Engineering, University College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran | Centre of Numerical Methods in Engineering, University of Tehran, Tehran, Iran

Note: [] Corresponding author. Tel.: +98 2161112225; Fax: +98 2166403808; E-mail: [email protected]

Abstract: Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

Keywords: Axially functionally graded materia, tapered beam element, free vibration, stability

DOI: 10.3233/SAV-2010-0589

Journal: Shock and Vibration, vol. 18, no. 5, pp. 683-696, 2011