Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation

Vu Duc Phuc, Tong Van Canh, Pham Van Lieu

Abstract


Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters allow to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA.

Keywords


dynamic vibration absorber; torsional excitation; optimazed parameters; rotary systems

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References


T. Asami, Y. Mizukawa, and T. Ise. Optimal design of double-mass dynamic vibration absorbers minimizing the mobility transfer function. Journal of Vibration and Acoustics, 140, (6), (2018). https://doi.org/10.1115/1.4040229.

H. Frahm. Device for damped vibration of bodies. U.S. Patent No. 989958, (1909).

J. Ormondroyd and J. P. Den Hartog. The theory of the dynamic vibration absorber. Trans. ASME, Applied Mechanics, 50, (1928), pp. 9–22.

J. P. Den Hartog. Mechanical vibrations. McGraw-Hill, New York, (1934).

J. Dayou. Fixed-points theory for global vibration control using vibration neutralizer. Journal of Sound and Vibration, 292, (3-5), (2006), pp. 765–776. https://doi.org/10.1016/j.jsv.2005.08.032.

K. Liu and J. Liu. The damped dynamic vibration absorbers: revisited and new result. Journal of Sound and Vibration, 284, (3-5), (2005), pp. 1181–1189. https://doi.org/10.1016/j.jsv.2004.08.002.

H. E. Kalehsar and N. Khodaie. Optimization of response of a dynamic vibration absorber forming part of the main system by the fixed-point theory. KSCE Journal of Civil Engineering, 22, (7), (2018), pp. 2354–2361. https://doi.org/10.1007/s12205-017-1237-y.

T. Asami, O. Nishihara, and A. M. Baz. Analytical solutions to H¥ and H2 optimization of dynamic vibration absorbers attached to damped linear systems. Journal of Vibration and Acoustics, 124, (2), (2002), pp. 284–295. https://doi.org/10.1115/1.1456458.

T. Asami and O. Nishihara. H2 optimization of the three-element type dynamic vibration absorbers. Journal of Vibration and Acoustics, 124, (4), (2002), pp. 583–592. https://doi.org/10.1299/kikaic.68.76.

O. Nishihara and T. Asami. Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors). Journal of Vibration and Acoustics, 124, (4), (2002), pp. 576–582. https://doi.org/10.1115/1.1500335.

Y. Shen, X. Wang, S. Yang, and H. Xing. Parameters optimization for a kind of dynamic vibration absorber with negative stiffness. Mathematical Problems in Engineering, 2016, (2016). https://doi.org/10.1155/2016/9624325.

S. H. Crandall andW. D. Mark. Random vibration in mechanical systems. Academic Press, London, (1963).

M. Zilletti, S. J. Elliott, and E. Rustighi. Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation. Journal of Sound and Vibration, 331, (18), (2012), pp. 4093–4100. https://doi.org/10.1016/j.jsv.2012.04.023.

H. Yamaguchi. Damping of transient vibration by a dynamic absorber. Trans. Jpn. Soc. Mech. Eng. Ser. C, 54, (499), (1988), pp. 561–568. https://doi.org/10.1299/kikaic.54.561.

T. Argentini, M. Belloli, and P. Borghesani. A closed-form optimal tuning of mass dampers for one degree-of-freedom systems under rotating unbalance forcing. Journal of Vibration and Acoustics, 137, (3), (2015). https://doi.org/10.1115/1.4029576.

P. Bisegna and G. Caruso. Closed-form formulas for the optimal pole-based design of tuned mass dampers. Journal of Sound and Vibration, 331, (10), (2012), pp. 2291–2314. https://doi.org/10.1016/j.jsv.2012.01.005.

A. G. Thompson. Optimizing the untuned viscous dynamic vibration absorber with primary system damping-a frequency locus method-reply. Journal of Sound and Vibration, 73, (3), (1980), pp. 469–472. https://doi.org/10.1016/0022-460X(80)90528-3.

E. Pennestri. An application of Chebyshev’s min–max criterion to the optimal design of a damped dynamic vibration absorber. Journal of Sound and Vibration, 217, (4), (1998), pp. 757–765. https://doi.org/10.1006/jsvi.1998.1805.

K. Liu and G. Coppola. Optimal design of damped dynamic vibration absorber for damped primary systems. Transactions of the Canadian Society for Mechanical Engineering, 34, (1), (2010), pp. 119–135. https://doi.org/10.1139/tcsme-2010-0008.

N. V. Khang, T. Q. Loc, and N. A. Tuan. Parameter optimization of tuned mass damper for three-degree-of-freedom vibration systems. Vietnam Journal of Mechanics, 35, (3), (2013), pp. 215–224. https://doi.org/10.15625/0866-7136/35/3/3315.

N. D. Anh and N. C. Sang. On the optimal control force applied to tuned mass dampers for multi-degree-of-freedom systems. Vietnam Journal of Mechanics, 26, (1), (2004), pp. 1–10. https://doi.org/10.15625/0866-7136/26/1/5682.

N. D. Anh, N. H. Hai, N. X. Nguyen, D. V. Hieu, and P. T. T. My. Weighted averaging technique for the design of dynamic vibration absorber installed in damped primary structures. Vietnam Journal of Mechanics, 40, (2), (2018), pp. 155–162. https://doi.org/10.15625/0866-7136/10732.




DOI: https://doi.org/10.15625/0866-7136/14897 Display counter: Abstract : 188 views. PDF : 86 views.

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