Open Access Open Access  Restricted Access Subscription Access

Weighted averaging technique for the design of dynamic vibration absorber installed in damped primary structures

N. D. Anh, N. H. Hai, N. X. Nguyen, D. V. Hieu, P. T. T. My

Abstract


The dynamic vibration absorber (DVA) has been widely applied in various technical fields. This paper presents a simple approach to determine a closed-form expression for the tuning ratio of a DVA attached to a damped primary structure. The result is obtained by using the so-called weighted averaging technique of the equivalent linearization method proposed by the first author. The values of the tuning ratio given in this paper are compared with those obtained numerically as well as the ones obtained from other authors. The comparison shows the reliability of the method given in this study.


Keywords


dynamic vibration absorber; tuned mass damper; analytical formula; damped structures

Full Text:

PDF

References


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

J. Ormondroyd and J. Den Hartog. The theory of the dynamic vibration absorber. Transactions of ASME, Journal of Applied Mechanics, 50, (7), (1928), pp. 9–22.

F. Casciati and F. Giuliano. Performance of multi-TMD in the towers of suspension bridges. Journal of Vibration and Control, 15, (6), (2009), pp. 821–847. doi:10.1177/1077546308091455.

N. D. Anh, H. Matsuhisa, L. D. Viet, and M. Yasuda. Vibration control of an inverted pendulum type structure by passive mass–spring-pendulum dynamic vibration absorber. Journal of Sound and Vibration, 307, (1), (2007), pp. 187–201. doi:10.1016/j.jsv.2007.06.060.

P.Warnitchai and N. Hoang. Optimal placement and tuning of multiple tuned mass dampers for suppressing multi-mode structural response. Smart Structures and Systems, 2, (1), (2006), pp. 1–24. doi:10.12989/sss.2006.2.1.001.

J. Den Hartog. Mechanical vibrations. McGraw-Hill, New York, (1956).

T. Ioi and K. Ikeda. On the dynamic vibration damped absorber of the vibration system. Bulletin of the Japanese Society of Mechanical Engineering, 21, (151), (1978), pp. 64–71. doi:10.1299/jsme1958.21.64.

S. E. Randall, D. M. Halsted, and D. L. Taylor. Optimum vibration absorbers for linear damped systems. Journal of Mechanical Design, 103, (4), (1981), pp. 908–913. doi:10.1115/1.3255005.

A. G. Thompson. Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system. Journal of Sound and Vibration, 77, (3), (1981), pp. 403–415. doi:10.1016/s0022-460x(81)80176-9.

G. B. Warburton. Optimum absorber parameters for various combinations of response and excitation parameters. Earthquake Engineering & Structural Dynamics, 10, (3), (1982), pp. 381–401. doi:10.1002/eqe.4290100304.

Y. Fujino and M. Abe. Design formulas for tuned mass dampers based on a perturbation technique. Earthquake Engineering & Structural Dynamics, 22, (10), (1993), pp. 833–854. doi:10.1002/eqe.4290221002.

A. Ghosh and B. Basu. A closed-form optimal tuning criterion for TMD in damped structures. Structural Control and Health Monitoring, 14, (4), (2007), pp. 681–692. doi:10.1002/stc.176.

N. D. Anh and N. X. Nguyen. Extension of equivalent linearization method to design of TMD for linear damped systems. Structural Control and Health Monitoring, 19, (6), (2012), pp. 565–573. doi:10.1002/stc.446.

N. D. Anh. Dual approach to averaged values of functions: a form for weighting coefficient. Vietnam Journal of Mechanics, 37, (2), (2015), pp. 145–150. doi:10.15625/0866-7136/37/2/6206.

N. D. Anh, N. Q. Hai, and D. V. Hieu. The equivalent linearization method with a weighted averaging for analyzing of nonlinear vibrating systems. Latin American Journal of Solids and Structures, 14, (9), (2017), pp. 1723–1740. doi:10.1590/1679-78253488.




DOI: https://doi.org/10.15625/0866-7136/10732

Refbacks

  • There are currently no refbacks.


 

                      

Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam

Tel: (+84) 24 3791 7103

Email: vjmech@vjs.ac.vn