A comprehensive review on dual approach to the vibration analysis: Some dual techniques and application
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https://doi.org/10.15625/0866-7136/14699Keywords:
dual approach, dual technique, forward - return dual, global-local dual, weighted averaging dualAbstract
This paper reviews key ideas of the researches on the dual approach to the vibration analysis. Three types of dual techniques, namely, forward - return dual technique, global-local dual technique, weighted averaging dual technique for the problem of equivalent replacement are summarized. Different implements and realizations of dual techniques to nonlinear vibration analysis and design of dynamic absorbers are reviewed. Finally, the challenging issues based on the dual techniques are discussed. A number of possibilities for developing analytical techniques related to dual techniques are proposed. The review shows that the dual approach is an appropriate one and the dual techniques are effective tools for studying random and deterministic nonlinear vibrational systems.
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References
A. Fidlin. Nonlinear oscillations in mechanical engineering. Springer Science & Business Media, (2005).
N. D. Anh. Duality in the analysis of responses to nonlinear systems. Vietnam Journal of Mechanics, 32, (4), (2010), pp. 263–266. https://doi.org/10.15625/0866-7136/32/4/294.
N. D. Anh. Dual approach to averaged values of functions. Vietnam Journal of Mechanics, 34, (3), (2012), pp. 211–214. https://doi.org/10.15625/0866-7136/34/3/2361.
N. D. Anh, N. N. Hieu, and N. N. Linh. A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation. Acta Mechanica, 223, (3), (2012), pp. 645–654. https://doi.org/10.1007/s00707-011-0582-z.
N. D. Anh, V. L. Zakovorotny, N. N. Hieu, and D. V. Diep. A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation. Acta Mechanica, 223, (12), (2012), pp. 2667–2684. https://doi.org/10.1007/s00707-012-0738-5.
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. https://doi.org/10.1002/stc.446.
N. D. Anh and N. X. Nguyen. Design of TMD for damped linear structures using the dual criterion of equivalent linearization method. International Journal of Mechanical Sciences, 77, (2013), pp. 164–170. https://doi.org/10.1016/j.ijmecsci.2013.09.014.
N. D. Anh, N. X. Nguyen, and L. T. Hoa. Design of three-element dynamic vibration absorber for damped linear structures. Journal of Sound and Vibration, 332, (19), (2013), pp. 4482–4495. https://doi.org/10.1016/j.jsv.2013.03.032.
N. D. Anh, L. X. Hung, and L. D. Viet. Dual approach to local mean square error criterion for stochastic equivalent linearization. Acta Mechanica, 224, (2), (2013), pp. 241–253. https://doi.org/10.1007/s00707-012-0751-8.
N. D. Anh, N. N. Linh, and N. Q. Hai. A weighted dual criterion for the problem of equivalent replacement. In Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Modeling, and Analysis, Liverpool, UK, (2014), pp. 1913–1922, https://doi.org/10.1061/9780784413609.191.
N. D. Anh and N. N. Linh. A weighted dual criterion for stochastic equivalent linearization method. Vietnam Journal of Mechanics, 36, (4), (2014), pp. 307–320. https://doi.org/10.15625/0866-7136/36/4/5106.
N. D. Anh, I. Elishakoff, and N. N. Hieu. Extension of the regulated stochastic linearization to beam vibrations. Probabilistic Engineering Mechanics, 35, (2014), pp. 2–10. https://doi.org/10.1016/j.probengmech.2013.07.001.
N. D. Anh and N. X. Nguyen. Design of non-traditional dynamic vibration absorber for damped linear structures. Journal of Mechanical Engineering Science, 228, (1), (2014), pp. 45–55. https://doi.org/10.1177/0954406213481422.
N. D. Anh, L. X. Hung, L. D. Viet, and N. C. Thang. Global–local mean square error criterion for equivalent linearization of nonlinear systems under random excitation. Acta Mechanica, 226, (9), (2015), pp. 3011–3029. https://doi.org/10.1007/s00707-015-1332-4.
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. https://doi.org/10.15625/0866-7136/37/2/6206.
N. M. Triet. Extension of dual equivalent linearization technique to flutter analysis of two dimensional nonlinear airfoils. Vietnam Journal of Mechanics, 37, (3), (2015), pp. 217–230. https://doi.org/10.15625/0866-7136/37/3/6474.
N. D. Anh and N. X. Nguyen. Research on the design of non-traditional dynamic vibration absorber for damped structures under ground motion. Journal of Mechanical Science and Technology, 30, (2), (2016), pp. 593–602. https://doi.org/10.1007/s12206-016-0113-x.
N. D. Anh, N. X. Nguyen, and N. H. Quan. Global-local approach to the design of dynamic vibration absorber for damped structures. Journal of Vibration and Control, 22, (14), (2016), pp. 3182–3201. https://doi.org/10.1177/1077546314561282.
N. D. Anh, I. Elishakoff, and N. N. Hieu. Generalization of Seide’s problem by the regulated stochastic linearization technique. Meccanica, 52, (4-5), (2017), pp. 1003–1016. https://doi.org/10.1007/s11012-016-0421-3.
N. D. Anh, N. N. Hieu, P. N. Chung, and N. T. Anh. Thermal radiation analysis for small satellites with single-node model using techniques of equivalent linearization. Applied Thermal Engineering, 94, (2016), pp. 607–614. https://doi.org/10.1016/j.applthermaleng.2015.10.139.
P. N. Chung, N. D. Anh, N. N. Hieu, and D. V. Manh. Extension of dual equivalent linearization to nonlinear analysis of thermal behavior of a two-node model for small satellites in Low Earth Orbit. International Journal of Mechanical Sciences, 133, (2017), pp. 513–523. https://doi.org/10.1016/j.ijmecsci.2017.09.011.
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. https://doi.org/10.1590/1679-78253488.
N. D. Anh and N. N. Linh. A weighted dual criterion of the equivalent linearization method for nonlinear systems subjected to random excitation. Acta Mechanica, 229, (3), (2018), pp. 1297–1310. https://doi.org/10.1007/s00707-017-2009-y.
D. V. Hieu and N. Q. Hai. Analyzing of nonlinear generalized Duffing oscillators using the equivalent linearization method with a weighted averaging. Asian Research Journal of Mathematics, (2018), pp. 1–14. https://doi.org/10.9734/ARJOM/2018/40684.
D. V. Hieu, N. Q. Hai, and D. T. Hung. The equivalent linearization method with a weighted averaging for solving undamped nonlinear oscillators. Journal of Applied Mathematics, 2018, (2018). https://doi.org/10.1155/2018/7487851.
V.-H. Dang, D.-A. Nguyen, M.-Q. Le, and Q.-H. Ninh. Nonlinear vibration of microbeams based on the nonlinear elastic foundation using the equivalent linearization method with a weighted averaging. Archive of Applied Mechanics, (2019), pp. 1–20. https://doi.org/10.1007/s00419-019-01599-w.
V.-H. Dang, D.-A. Nguyen, M.-Q. Le, and T.-H. Duong. Nonlinear vibration of nanobeams under electrostatic force based on the nonlocal strain gradient theory. International Journal of Mechanics and Materials in Design, (2019), pp. 1–20. https://doi.org/10.1007/s10999-019-09468-8.
J. Lee Rodgers and W. A. Nicewander. Thirteen ways to look at the correlation coefficient. The American Statistician, 42, (1), (1988), pp. 59–66. https://doi.org/10.1080/00031305.1988.10475524.
J. B. Roberts and P. D. Spanos. Random vibration and statistical linearization. Dover Publications Inc., New York, (2003).
N. D. Anh and M. Di Paola. Some extensions of Gaussian equivalent linearization. In International Conference on Nonlinear Stochastic Dynamics, (1995), pp. 5–15.
L. X. Hung. Approximate analysis of some two-degree-of-freedom nonlinear random systems by an extension of Gaussian equivalent linearization. Vietnam Journal of Mechanics, 23, (2), (2001), pp. 95–109. https://doi.org/10.15625/0866-7136/9943.
N. D. Anh and L. X. Hung. An improved criterion of Gaussian equivalent linearization for analysis of non-linear stochastic systems. Journal of Sound and Vibration, 1, (268), (2003), pp. 177–200. https://doi.org/10.1016/S0022-460X(03)00246-3.
N. Krylov and N. Bogoliubov. Introduction to nonlinear mechanics. Princeton University Press, New York, (1943).
S. H. Crandall. A half-century of stochastic equivalent linearization. Structural Control and Health Monitoring, 13, (1), (2006), pp. 27–40. https://doi.org/10.1002/stc.129.
I. Elishakoff and S. H. Crandall. Sixty years of stochastic linearization technique. Meccanica, 52, (1-2), (2017), pp. 299–305. https://doi.org/10.1007/s11012-016-0399-x.
L. Socha. Linearization methods for stochastic dynamic system. Lecture Notes in Physics, Springer, Berlin, (2008).
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