Affiliations: C. S. Mott Engineering and Science Center, Department
of Mechanical Engineering, Kettering University, Flint, MI, USA
Note: [] Corresponding author: Arnaldo J. Mazzei, Jr., C. S. Mott
Engineering and Science Center, Department of Mechanical Engineering, Kettering
University, 1700 University Avenue, Flint, MI 48504, USA. Tel.: +1 810 762
7878; Fax: +1 810 762 7860; E-mail: amazzei@kettering.edu
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
