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Structural Engineering and Mechanics
  Volume 45, Number 1, January10 2013, pages 069-93

On the dynamics of rotating, tapered, visco-elastic beams with a heavy tip mass
Serkan Zeren and Metin Gurgoze

    The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton\'s Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.
Key Words
    rotating tapered beam; Bernoulli-Euler beam; Kelvin-Voigt material; heavy tip mass; offset
Serkan Zeren: Department of Mechanical Engineering, Yeditepe University, Istanbul, Turkey
Metin Gurgoze: 2Faculty of Mechanical Engineering, Technical University of Istanbul, Istanbul, Turkey

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