An improved beam element for beams with variable axial parameters

Article type: Research Article

Authors: He, Peng | Liu, Zhansheng | Li, Chun

Affiliations: School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China

Note: [] Corresponding author: Peng He, School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China. Tel.: +86 0451 8641 3794; Fax: +86 0451 8641 3242; E-mail: [email protected]

Abstract: The traditional beam element was improved to consider the variable axial parameters. The variable axial parameters were formulated in terms of a power series, and the general forms of elementary mass and stiffness matrices which depend on the power order were derived. The mass and stiffness matrices of the improved beam element were obtained in terms of an elementary matrix series. The beam elements for various tapered beams and a beam under linearly axial temperature distribution were derived. The vibrations of the beams with various taper shapes were studied and the variations of natural frequencies and modal shapes were investigated. A uniform beam under linearly axial temperature distribution was modeled and studied. The influences of axial temperature difference on the natural frequencies and modal shapes were investigated. Results show that the improved beam element could consider the variable axial parameters of beam conveniently.

Keywords: Variable axial parameters, transverse vibration, tapered beam, temperature, finite element method

DOI: 10.3233/SAV-130771

Journal: Shock and Vibration, vol. 20, no. 4, pp. 601-617, 2013