Abstract
This paper is on flap-wise vibrations of centrifugally stiffened axially functionally graded beams with multiple lumped masses including rotary inertia effects. Material properties are defined along beams’ length using the function appropriate to the power law distribution. Energy expressions of Euler–Bernoulli beam model are stated for flexural vibrations of beam with additional multiple masses rotating around a hub. Energy formulations are discretised to apply Rayleigh–Ritz solution method which uses admissible polynomial mode shape function. Analyses are conducted by changing number, size and inertias of additional masses, taper ratios of beam, rotating speed and radius of hub and the power of distribution function of beam material. Non-dimensional parameters are used to reflect results that are validated by those given in current literature. Unique results are also given for the homogeneous and functionally graded beam rotating with multiple masses. Effects of varying parameters and advantages/shortcomings of present solution are reflected and discussed.
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References
K.H. Low, A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses. Int. J. Mech. Sci. 42, 1287–1305 (2000)
K.H. Low, Natural frequencies of a beam-mass system in transverse vibration: Rayleigh estimation versus eigenanalysis solutions. Int. J. of Mech. Sci. 45, 981–993 (2003)
S. Maiz, D.V. Bambill, C.A. Rossit, P.A.A. Laura, Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: exact solution. J. Sound Vib. 303, 895–908 (2007)
J. Chung, H.H. Yoo, Dynamic analysis of a rotating cantilever beam by using the finite element method. J. Sound Vib. 249, 147–164 (2002)
J.B. Yang, L.J. Jiang, D.C.H. Chen, Dynamic modelling and control of a rotating Euler-Bernoulli beam. J. Sound Vib. 274, 863–875 (2004)
J.R. Banerjee, Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. J. Sound Vib. 233(5), 857–875 (2000)
H.H. Yoo, S.H. Shin, Vibration analysis of rotating cantilever beams. J. Sound Vib. 212(5), 807–828 (1998)
R.B. Bhat, Transverse vibrations of a rotating uniform cantilever with tip mass as predicted by using beam characteristics orthogonal polynomials in the Rayleigh–Ritz method. J. Sound Vib. 105, 199–210 (1986)
Y.A. Khulief, Vibration frequencies of a rotating tapered beam with end mass. J. Sound Vib. 134, 87–97 (1989)
Y. Huang, X.-F. Li, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. J. Sound Vib. 329, 2291–2303 (2010)
H. Zarrinzadeh, R. Attarnejad, A. Shahba, Free vibration of rotating axially functionally graded tapered beams. Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 226, 363–379 (2012)
S. Rajasekaran, Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams. Int. J. Mech. Sci. 74, 15–31 (2013)
K. Mazanoglu, S. Guler, Flap-wise and chord-wise vibrations of axially functionally graded tapered beams rotating around a hub. Mech. Syst. Sign. Process. 89, 97–107 (2017)
J. Fang, D. Zhou, Free vibration analysis of rotating axially functionally graded-tapered beams using Chebyshev–Ritz method. Mater. Res. Innov. 19, 1255–1262 (2015)
Acknowledgements
The research topic in this work is supported by “The Scientific and Technological Research Council of Turkey (TUBITAK)” within the framework of national project as “1002—Short Term R&D Funding Program” (Project no: 215M756).
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Mazanoğlu, K., Karakuzu, T. (2018). Flap-Wise Vibrations of Axially Functionally Graded and Centrifugally Stiffened Beams with Multiple Masses Having Rotary Inertia. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS-2017. Springer Proceedings in Physics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-69823-6_7
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DOI: https://doi.org/10.1007/978-3-319-69823-6_7
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