An engineering application of the h-p version of the finite elements method to the dynamics analysis of a symmetrical on-board rotor
Keywords:
Symmetrical rotor, h-p version of FEM, on-board rotor, rotor dynamics, base excitationAbstract
The h-p hybrid finite element method is used in this paper for the dynamic analysis of a symmetrical on-board rotor on mobile dimensionally stable supports. The disc and the bearings are assumed to be rigid, with deformable shaft, the material is isotropic. A three-dimensional beam element is used for the discretization of the rotor. In the standard h-version of the finite element, the used shape functions are cubic Hermit, which respect the boundary conditions in all directions, the shape functions-h are modified so they can make the combination between K-orthogonal polynomial shape functions facilitating combination to use the h-p version of the finite element method. Energy method is used for the determination of energy for the entire rotor system. The equations of motion of the rotor system are determined by the Lagrange method. The calculation steps for linear dynamic behaviour of on-board rotor system analysis are grouped in an application created using MATLAB programming language and validated with the work done previously by the classic version of the finite element method. In this paper, we make a comparison of the natural frequencies of on-board rotor system, obtained by the h-p version of the finite element method with version h.
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References
Babuska, I., & Guo, B. Q. 1992. The h, p and h-p version of the finite element method: Basis
theory and applications. Advances in Engineering Software, 15, 159–174.
Babuška, I., & Suri, M. (1987). The h-p version of the finite element method with quasiuniform
meshes. RAIRO – Modélisation mathématique et analyse numérique, 21, 199–238.
Banerjee, J. R. (2000). Free vibration of centrifugally stiffened uniform and tapered beams using
the dynamic stiffness method. Journal of Sound and Vibration, 233, 857–875.
Bardell, N. S. (1996). An engineering application of the h-p version of the finite element method
to the static analysis of a Euler-Bernoulli beam. Computers & Structures, 59, 195–211.
Bokaian, A. (1948). Natural frequencies of beams under compressive axial load. Journal of
Sound and Vibration, 126, 49–65.
Boukhalfa, A., & Hadjoui, A. (2010). Free vibration analysis of an embarked rotating composite
shaft using the h-p version of the FEM. Latin American Journal of Solids and Structures, 7(2).
Chen, L. W., & Ku, D. M. (1992). Dynamic stability of a cantilever shaft-disk system. Journal
of Vibration and Acoustics Transaction of the American Society of Mechanics Engineers, 114,
–329.
Chen, L. W., & Sheu, H. C. (1998). Stability behavior of a shaft-disk system subjected to
longitudinal force. Journal of Propulsion and Power, 14, 375–383.
Choi II, S., Pierre, C., Ulsoy, A. G. (1995). Consistent modeling of rotating Timoshenko shaft
subject to axial loads. Journal of Sound and Vibration and Acoustics, 182, 759–773.
Dakel, M. (2013). Steady-state dynamic behaviour of an on-board rotor under combined base
motions. Journal of Vibration and Control, 20, 2254–2287. doi:10.1177/1077546313483791
Duchemin, M., Berlioz, A., & Ferraris, G. (2006). Dynamic behavior and stability of a rotor
under base excitation. Journal of Vibration and Acoustics, 128, 576–585.
Eshienman, R. L., & Eubanks, R. A. (1967). On the critical speeds of a continuous shaft-disk
system. Journal of Engineering for Industry, 80, 645–652.
Green, R. B. (1948). Gyroscopic effects on the critical speeds of flexible rotors. Transaction of
the American society of Mechanic Engineers, 70, 309–376.
Heuveline, V., & Rannacher. 2003. Duality-based adaptively in h-p-finite element method.
Journal of Numerical Mathematics, 11, 95–113. doi:10.1515/156939503766614126
Khader, N. (1995). Stability of rotating shafts loaded by follower axial force and torque load.
Journal of Sound and Vibration, 182, 759–773.
Lalanne, M., & Ferraris, G. (1998). Rotor dynamics prediction in engineering (2nd ed.).
Chichester: Wiley. 254 p.
Lin, S. C., & Hsiao, K. M. (2001). Vibration analysis of a rotating Timoshenko beam. Journal
of Sound and Vibration, 240, 303–322.
Nelson, H. D., & McVaugh, J. M. (1976). The dynamics of rotor-bearing systems using finite
elements. ASME Journal of Engineering for Industry, 98, 593–600.
Peano, A. (1976). Hierarchies of conforming finite elements for plane elasticity and plate
bending. Computers & Mathematics with Applications, 2, 211–224.
Rao, S. S. (1983). Rotor dynamics. New York, NY: Wiley.
Szabo, B. (1985a). A PROB theoretical manual release1. St Louis, MO: Technologies Corp.
Szabo, B. (1985b). A FIESTA theoretical manual release1. St Louis, MO: Technologies Corp.
