Duality in the analysis of responses to nonlinear systems

Nguyen Dong Anh
Author affiliations

Authors

  • Nguyen Dong Anh Institute of Mechanics, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/32/4/294

Abstract

The paper provides a new view on the averaging procedure and equivalent linearization in the study of nonlinear mechanics. It is shown that the duality of those techniques can be used to obtain better approximate solutions or to separate the original nonlinear systems subjected to periodic and random excitations into deterministic and stochastic ones.

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Published

22-12-2010

How to Cite

Dong Anh, N. (2010). Duality in the analysis of responses to nonlinear systems. Vietnam Journal of Mechanics, 32(4), 263–266. https://doi.org/10.15625/0866-7136/32/4/294

Issue

Section

Research Article
N. D. Anh, L. X. Hung, L. D. Viet (2013)
Dual approach to local mean square error criterion for stochastic equivalent linearization. Acta Mechanica, 224(2), 241.
10.1007/s00707-012-0751-8
N. D. Anh, Nguyen Ngoc Linh, Tran Tuan Long, Nguyen Cao Thang, Anh Tay Nguyen, I. Elishakoff (2023)
Extension of dual equivalent linearization to analysis of deterministic dynamic systems. Part 1: single-parameter equivalent linearization. Nonlinear Dynamics, 111(2), 997.
10.1007/s11071-022-07894-6
N. D. Anh, N. X. Nguyen (2016)
Research on the design of non-traditional dynamic vibration absorber for damped structures under ground motion. Journal of Mechanical Science and Technology, 30(2), 593.
10.1007/s12206-016-0113-x
ND Anh, NX Nguyen (2014)
Design of non-traditional dynamic vibration absorber for damped linear structures. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228(1), 45.
10.1177/0954406213481422
N. D. Anh, V. L. Zakovorotny, N. N. Hieu, D. V. Diep (2012)
A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation. Acta Mechanica, 223(12), 2667.
10.1007/s00707-012-0738-5
Xuan-Truong Vu, Duy-Chinh Nguyen, Doan-Dien Khong, Van-Canh Tong (2018)
Closed-form solutions to the optimization of dynamic vibration absorber attached to multi-degrees-of-freedom damped linear systems under torsional excitation using the fixed-point theory. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 232(2), 237.
10.1177/1464419317725216
N.D. Anh, V.L. Zakovorotny, D.N. Hao (2014)
Response analysis of Van der Pol oscillator subjected to harmonic and random excitations. Probabilistic Engineering Mechanics, 37, 51.
10.1016/j.probengmech.2014.05.001
N. D. Anh, N. N. Hieu, N. N. Linh (2012)
A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation. Acta Mechanica, 223(3), 645.
10.1007/s00707-011-0582-z
Vu Duc Phuc, Van-The Tran, Nguyen Van Quyen (2019)
A novel design of the dynamic vibration absorbers for damped main systems under torsional excitation using least squares estimation of the equivalent linearization method. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 233(1), 60.
10.1177/1464419318779339
N.D. Anh, N.X. Nguyen, L.T. Hoa (2013)
Design of three-element dynamic vibration absorber for damped linear structures. Journal of Sound and Vibration, 332(19), 4482.
10.1016/j.jsv.2013.03.032
N. D. Anh, N. N. Linh (2018)
A weighted dual criterion of the equivalent linearization method for nonlinear systems subjected to random excitation. Acta Mechanica, 229(3), 1297.
10.1007/s00707-017-2009-y
N.D. Anh, N.X. Nguyen (2013)
Design of TMD for damped linear structures using the dual criterion of equivalent linearization method. International Journal of Mechanical Sciences, 77, 164.
10.1016/j.ijmecsci.2013.09.014
Genbei Zhang, Chaoping Zang, Michael I. Friswell (2019)
Identification of weak nonlinearities in MDOF systems based on reconstructed constant response tests. Archive of Applied Mechanics, 89(10), 2053.
10.1007/s00419-019-01559-4
N. D. Anh, L. X. Hung, L. D. Viet, N. C. Thang (2015)
Global–local mean square error criterion for equivalent linearization of nonlinear systems under random excitation. Acta Mechanica, 226(9), 3011.
10.1007/s00707-015-1332-4