On the effect of functionally graded materials on resonances of rotating beams

Article type: Research Article

Authors: Mazzei, Jr., Arnaldo J.

Affiliations: C.S. Mott Engineering and Science Center, Department of Mechanical Engineering, Kettering University, Flint, MI, USA

Note: [] Corresponding author. Tel.: +1 810 762 7878; Fax: +1 810 762 7860; E-mail: [email protected]

Abstract: Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

Keywords: Axially rotating beams, FGM, spatially varying material properties

DOI: 10.3233/SAV-2011-0661

Journal: Shock and Vibration, vol. 19, no. 4, pp. 707-718, 2012