Vibration Study of Rotating Rigid Hub and a Flexible Composite Beam under Simultaneous Primary-internal Resonance
Asian Research Journal of Mathematics, Volume 19, Issue 8,
In this paper, the vibration of a composite system consisting of a rotating rigid hub and a flexible thin-walled beam is considered and studied. The equation of motion is derived in the previous work of Warminski and Latalski. The method of multiple scale technique has been applied to obtain frequency response equations near the simultaneous internal and primary resonance case in the absence of the acceleration of the hub. The vibration stability at this resonance case is investigated from the frequency response equations and studied using Liapunov’s methods. The effects of changes in selected structural parameters on the vibrating system behavior are investigated and studied numerically. Through the performed studies of the effects of changes in selected system a shift of the steady state amplitudes and the multi-valued of the bent curves are observed and the steady state amplitudes of the beam and hub have decreasing in the instability regions for natural frequencies. Finally, a comparison with the papers of previously published work is reported.
- Simultaneous primary resonance
- frequency response curves
- system stability
- jump phenomenon
How to Cite
Subrahmanyam K, Kulkarni S, Rao J. Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method. Journal of Sound and Vibration. 1981; 75(1):17-36.
Dokumaci E. An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry. Journal of Sound and Vibration. 1987; 119(3):443-449.
Bishop R, Cannon S, Miao S. On coupled bending and torsional vibration of uniform beams. Journal of Sound and Vibration. 1989; 131(3):457–464.
Vasiliev V. Mechanics of composite structures. CRC Press.1993; 1st ed.
Lee Y, Sheu J. Free vibrations of a rotating inclined beam. Journal of Appl. Mech. 2007; 74:406-414.
Wen L, Kuo H. Free vibration analysis of rotating Euler beams at high angular velocity. Journal of Computers and Structures. 2010; 88:991-1001.
Kamel M, Amer Y. Response of parametrically excited one degree of freedom system with nonlinear damping and stiffness. Physica Scripta. 2002; 66:410–416.
Kamel M, Eissa M, Al-mandouh A. The response and stability of a rotor arm simulated by a cantilever beam. International Journal of Robotics Research and Development. 2014; 4:1-16.
Nayfeh A, Nayfeh S. Non-linear normal modes of a continuous system with quadratic nonlinearities. Journal of Vibration and Acoustics. 1994; 117:199–205.
Pesheck E, Pierre C, Shaw S. Modal reduction of a non-linear rotating beam through normal modes. Journal of Vibration and Acoustics. 2002; 124:229–236.
Nayfeh A, Chin C, Nayfeh S. Non-linear normal modes of a cantilever beam. Journal of Vibration and Acoustics. 1995; 117:477–481.
Petrov E, Ewins D. Effects of damping and varying contact area at blade-disk joints in forced response analysis of bladed disk assemblies. Journal of Turbomachinery. 2006; 8(2):403- 410.
He B, Ouyang H, Ren X. Dynamic response of a simplified turbine blade model with under-platform dry friction dampers considering normal load variation. Applied Sciences. 2017; 7(3):228.
Qin Z, Han Q, Chu F. Bolt loosening at rotating joint interface and its influence on rotor dynamics. Engineering Failure Analysis. 2016; 59:456–466.
Qin Z, Yang Z, Zu J. Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. International Journal of Mechanical Sciences. 2018; 142(143):127–139.
Li B, Ma H, Yu X. Nonlinear vibration and dynamic stability analysis of rotor-blade system with nonlinear supports. Archive of Applied Mechanics. 2019; 89(7):1375-1402.
Cao D, Gong X, Wei D. Nonlinear vibration characteristics of a flexible blade with friction damping due to tiprub. Shock and Vibration. 2011; 18(1–2):105–114.
Cao D, Liu B, Yao M. Free vibration analysis of a pretwisted sandwich blade with thermal barrier coating layers. Science China. Technological Sciences. 2017; 60(11):1747-1761.
Das K, Ray C, Pohit G. Large amplitude free vibration analysis of a rotating beam with non-linear spring and mass system. Journal of Vibration and Control. 2005; 11(12):1511-1533.
Xue X, Tang J. Vibration control of nonlinear rotating beam using piezoelectric actuator and sliding mode approach. Journal of Vibration and Control. 2008; 14(6):885-908.
Pohit G, Mallik A, Venkatesan C. Free out-of-plane vibration of a rotating beam with non-linear elastomeric constraints. Journal of Sound and Vibration. 1999; 220(1):1–25.
Pohit G, Venkatesan C, Mallik A. Elastomeric damper model and limit cycle oscillation in bearingless helicopter rotor blade. Journal of Aircraft. 2000; 37(5):923–926.
Pohit G, Venkatesan C, Mallik A. Influence of non-linear elastomer on isolated lag dynamics and rotor/fuselage aeromechanical stability. Journal of Aircraft. 2004; 41(6):1449– 1464.
Avramov K, Pierre C, Shyriaieva N. Flexural-flexural-torsional nonlinear vibrations of pre-twisted rotating beams with asymmetric cross-sections. Journal of Vibration and Control. 2007; 13(4):329–364.
Avramov K, Galas O, Morachkovskii O, Pierreñ C. Analysis of flexural- flexural torsional nonlinear vibrations of twisted rotating beams with cross-sectional deplanation. Strength of Materials. 2009; 41(2):200-208.
Dakel M, Baguet S, Dufour R. Steady-state dynamic behavior of an on-board rotor under combined base motions. Journal of Vibration and Control. 2014; 2254–2287.
Arvin H, Bakhtiari-Nejad F. Nonlinear free vibration analysis of rotating composite Timoshenko Beams. Compos Struct. 2013; 96:29–43.
Georgiades F, Latalski J, Warminski J. Equations of motion of rotating composite beam with a non-constant rotation speed and an arbitrary preset angle. Meccanica. 2014; 49:1838-1858.
Luat DT, Thom DV, Thanh TT, Minh PV, Ke TV, Vinh PV. Mechanical analysis of bi-functionally sandwich nanobeams. Advances in Nano Research. 2021; 11(1):55- 71.
Thom DV, Doan DH, Minh PV, Tung NS. Finite element modelling for vibration response of cracked stiffened FGM plates. Vietnam Journal of Science and Technology. 2020; 58(1):119-129.
Wang B, Li XF. Flexoelectric effects on the natural frequencies for free vibration of piezoelectric nanoplates. J. Appl. Phys. 2021; 129(3).
Duc DH, Thom DV, Cong PH, Minh PV, Nguyen NX. Vibration and static buckling behavior of variable thickness flexoelectric nanoplates. Mechanics Based Design of Structures and Machines; 2022.
Nguyen HN, Nguyen TY, Tran KV, Tran TT, Nguyen TT, Phan VD, Do TV. A finite element model for dynamic analysis of triple-layer composite plates with layers connected by shear connectors subjected to moving load. Materials. 2019; 12(598):1-19.
Tho NC, Thom DV, Cong PH, Zenkour AM, Doan DH, Minh PV. Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer. Composite Structures. 2023; 305:116529.
Warminski J, Latalski J. Dynamics of rotating thin-walled cantilever composite beam excited by translational motion. Journal of Proceedings of the Institution of Mechanical Engineers. 2016; 144:1039-1046.
Warminski J, Latalski J, Rega G. Bending-twisting vibrations of a rotating hub-thin- walled composite beam system. Mathematics and Mechanics of Solids. 2017; 22(6):1303-1325.
Nayfeh A, Mook D. Nonlinear oscillations. Wiley, New York; 1995.
Nayfeh A. Perturbation methods. Wiley, New York; 1973.
Jeltsch R, Mansour M. Stability theory. Birkhäuser Verlag; 1995.
Erawaty N, Kasbawati A, Amir K. Stability analysis for routh-hurwitz condition using partial pivot. Journal of Physics: Conference Series. 2019; 1341:062017.
Abstract View: 31 times
PDF Download: 8 times