AN EQUIVALENT LINEARIZATION APPROACH TO THE DESIGN OF MULTIPLE DYNAMIC VIBRATION ABSORBERS BASED ON WEIGHTED DUAL CRITERION

Vu Duc Phuc; Do Huy Tung; Pham Van Lieu

Vu Duc Phuc Faculty of Mechanical Engineering, Hung Yen University of Technology and Education
Do Huy Tung Faculty of Electrical Engineering, Sao Do University
Pham Van Lieu Faculty of Mechanical Engineering, University of Economics – Technology for Industries

Keywords: Damped primary system, Equivalent linearization approach, multiple dynamic vibration absorbers, weighted dual criterion

Abstract

The multiple dynamic vibration absorbers systems (MDVA) are widely used to control harmful vibration of the damped system under harmonic excitation. The MDVA have more benefit than the single DVA such as portability and easy to install. This paper using equivalent linearization approach based on weighted dual criterion to obtain explicit formulas of optimal parameters of MDVA for damped primary systems. The numerical studies reveal accuracy of the equivalent linearization approach and optimal formula of MDVA in control vibration of damped primary system.

References

Igusa T, Xu K,‘’Vibration control using multiple tuned mass dampers’’. J Sound Vib, 175, 1994, pp. 491-503.

Fujino. Y, Sun. L.M, “Vibration Control by Multiple Tuned Liquid Dampers (MTLDs)”. Journal of Structural Engineering, Vol. 119 (12), 1993, pp. 3482-3500.

Zuo L, Nayfeh SA, “Optimization of the individual stiffness and damping parameters in multipletuned mass damper systems’’. ASME J Vib Acoust, 127, 2005, pp. 77-83.

Nguyen Van Khang, Vu Duc Phuc, Do The Duong, Nguyen Thi Van Huong, “A procedure for optimal design of a dynamic vibration absorber installed in the damped primary system based on Taguchi’s method’’. Vietnam Journal of Science and Technology, 56 (5), 2018, pp. 649-661.

Vu DP, Tran TV, Nguyen VQ, “A novel design of the dynamic vibration absorbers for damped main systems under torsional excitation using least squares estimation of the equivalent linearization method’’. Proc I Mech E, Part K: J Multi-body Dynamics, 233, 2018, pp. 60-70.

Nguyen DA, Nguyen XN, “Extension of equivalent linearization method to design of TMD for linear damped systems’’. Struct Control Health Monit, 19(6), 2012, pp. 565–573.

N. D. Anh, Short Communication, “Weighted dual approach to the problem of equivalent replacement’’. Vietnam journal of mechanics, Vol 35, No 2, 2013, pp. 169-173.

N.D. Anh, N.X. Nguyen, L.T. Hoa, “Design of three-element dynamic vibration absorber for damped linear structures’’. Journal of Sound and Vibration, 332, 2013, pp. 4482–4495.

Den Hartog JP, “Mechanical Vibrations’’, 1985, 4th ed, Dover, New York.

Vu Duc Phuc, “Optimal Control of Vibration by Multiple Dynamic Vibration’’, PhD thesis in Mechanics, 2020, Ha Noi University of science and technology.

Krylov N and Bogoliubov N, “Introduction to nonlinear mechanics’’, 1943, Princeton, NJ: Princeton University Press.

Caughey TK, “Response of Van der Pols oscillator to random excitations’’. Transactions of ASME, Journal of Applied Mechanics, 26, 1956, pp. 345–34.