Abstract
Reduction of whirling vibration amplitudes in rotordynamic systems resulting from unbalance force during the passage through the critical speeds is very important for preventing propagation of fatigue cracks, excessive noise and instability problems. In this paper, numerical investigations of passive targeted energy transfer (TET) to mitigate the whirling vibration amplitude in rotor systems at the critical speeds are performed by applying nonlinear energy sinks (NESs) to the rotor systems. The three-degree-of-freedom hollow shaft-NES system has been modeled based on Lagrange’s method. Numerical simulations have been performed to optimize the NES parameters in order to obtain the optimum performance for vibration reduction. The influence of critical parameters, including the angle between the unbalance mass and the NES, the NES damping and the unbalance mass on the NES performance in whirling vibration reduction, is also investigated. Additionally, the application of the NES is compared with that of the tuned mass damper (TMD). Numerical results show that the NES is able to efficiently reduce the resonant amplitude of the rotor systems when the stiffness and mass ratios are optimized appropriately. Furthermore, it is found that, unlike the NES, the TMD requires an offset distance from the shaft centerline to be able to reduce the resonant amplitude; otherwise, it fails in mitigating the whirling amplitude. Identifying this offset for the TMD requires pre-knowledge of the exact unbalance value and its eccentricity from the shaft centerline. However, the NES does not require a priori knowledge of the unbalance value which is an advantage of the NES compared to the TMD. The TMD, applied here with an offset distance able to mitigate the resonant vibration, only works as a balancer when positioned opposite to the location of the unbalance mass, which limits its application in vibration reduction of rotor systems.
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References
Samantaray, A.K., Bhattacharyya, R., Mukherjee, A.: An investigation into the physics behind the stabilizing effects of two-phase lubricants in journal bearings. J. Vib. Control 12, 425–442 (2006)
Starosvetsky, Y., Gendelman, O.V.: Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system. J. Sound Vib. 312, 234–256 (2008)
Pinkaew, T., Lukkunaprasit, P., Chatupote, P.: Seismic effectiveness of tuned mass dampers for damage reduction of structures, seismic effectiveness of tuned mass dampers for damage reduction. Eng. Struct. 25, 39–46 (2003)
Nagarajaiah, S., Varadarajan, N.: Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD. Eng. Struct. 27, 431–441 (2005)
Yue, Q., Zhang, L., Zhang, W., Kärnä, T.: Mitigating ice-induced jacket platform vibrations utilizing a TMD system. Cold Reg. Sci. Technol. 56, 84–89 (2009)
Frahm, H.: Device for damping vibrations of bodies, US Patent 989958 (1911)
Den Hartog, J.P.: Mechanical Vibrations, 4th edn. McGraw-Hill, New York (1956)
Vakakis, A.F., Gendelman, O., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems: I and II. Springer, Berlin (2008)
McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Experimental study of non-linear energy pumping occurring at a single fast frequency. Int. J. Nonlinear. Mech. 40, 891–899 (2005)
Gendelman, O.V., Sigalov, G., Manevitch, L.I., Mane, M., Vakakis, A.F., Bergman, L.A.: Dynamics of an eccentric rotational nonlinear energy sink. ASME J. Appl. Mech. 79(011012), 1–9 (2012)
Kerschen, G., Kowtko, J.J., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators. Nonlinear Dyn. 47, 285–309 (2007)
Bellet, R., Cochelin, B., Côte, R., Mattei, P.-O.: Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers. J. Sound Vib. 331, 5657–5668 (2012)
Wierschem, N., Quinn, D.D., Hubbard, S., AL-Shudeifat, M.A., McFarland, M., Luo, J., Fahnestock, L.A., Vakakis, A.F., Bergman, L.A., Spencer Jr, B.F.: Passive damping enhancement of a two-degree-of-freedom system through a strongly nonlinear two-degree-of-freedom attachment. J. Sound Vib. 331(25), 5393–5407 (2012)
Quinn, D.D., Wierschem, N., Hubbard, S., AL-Shudeifat, M.A., Ott, R.J., McFarland, D.M., Vakakis, A.F., Bergman, L.A.: Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments. J. Multi-body Dyn. 226(2), 122–146 (2012)
Gendelman, O.V.: Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. 25, 237–253 (2001)
Vakakis, A.F., Gendelman, O.V.: Energy pumping in nonlinear mechanical oscillators: part II resonance capture. ASME J. Appl. Mech. 68, 42–48 (2001)
Quinn, D.D., Gendelman, O.V., Kerschen, G., Sapsis, T.P., Bergman, L.A., Vakakis, A.F.: Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1: 1 resonance capture: part I. J. Sound Vib. 311, 1228–1248 (2008)
Vaurigaud, B., Manevitch, L.I., Lamarque, C.-H.: Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer. J. Sound Vib. 330, 2580–2595 (2011)
Gendelman, O.V.: Targeted energy transfer in systems with non-polynomial nonlinearity. J. Sound Vib. 315, 732–745 (2008)
Georgiades, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Shock isolation through passive energy pumping caused by non-smooth nonlinearities. Int. J. Bifurc. Chaos 15, 1989–2001 (2005)
Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Kerschen, G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50, 651–677 (2007)
Karayannis, I., Vakakis, A.F., Georgiades, F.: Vibro-impact attachments as shock absorbers. P. I. Mech. Eng. C.-J. Mech. 222(10), 1899–1908 (2008)
Sigalov, G., Gendelman, O.V., AL-Shudeifat, M.A., Manevitch, L.I., Vakakis, A.F., Bergman, L.A.: Resonance captures and targeted energy transfers in an inertially coupled rotational nonlinear energy sink. Nonlinear Dyn. 69, 1693–1704 (2012)
Sigalov, G., Gendelman, O.V., AL-Shudeifat, M.A., Manevitch, L.I., Vakakis, A.F., Bergman, L.A.: Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling. Chaos 22(1), 013118–013118-10 (2012)
Nucera, F., Iacono, F.L., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: part II experimental results. J. Sound Vib. 313, 57–76 (2008)
AL-Shudeifat, M.A., Wierschem, N., Quinn, D.D., Vakakis, A.F., Bergman, L.A., Spencer Jr, B.F.: Numerical and experimental investigation of a highly effective single-sided vibro-impact non-linear energy sink for shock mitigation. J. Nonlinear Mech. 52, 96–109 (2013)
Samantaray, A.K.: Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects. Nonlinear Dyn. 56, 443–451 (2009)
Samantaray, A.K., Dasgupta, S.S., Bhattacharyya, R.: Sommerfeld effect in rotationally symmetric planar dynamical systems. Int. J. Eng. Sci. 48, 21–36 (2010)
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This work was funded by the National Natural Science Foundation of China (#71271068).
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Guo, C., AL-Shudeifat, M.A., Vakakis, A.F. et al. Vibration reduction in unbalanced hollow rotor systems with nonlinear energy sinks. Nonlinear Dyn 79, 527–538 (2015). https://doi.org/10.1007/s11071-014-1684-7
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DOI: https://doi.org/10.1007/s11071-014-1684-7