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Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

Luu Xuan Hung, Nguyen Cao Thang

Abstract


The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi-degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two-degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).


Keywords


probability; random; frequency response function; iteration method; mean square

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References


T. K. Caughey. Equivalent linearization techniques. The Journal of the Acoustical Society of America, 35, (11), (1963), pp. 1706–1711. https://doi.org/10.1121/1.1918794.

T. K. Caughey. Response of a nonlinear string to random loading. Journal of Applied Mechanics, 26, (3), (1959), pp. 341–344.

L. Socha. Linearization methods for stochastic dynamic systems. Lecture Notes in Physics, Springer, Berlin, (2008).

X. Zhang, I. Elishakoff, and R. Zhang. A stochastic linearization technique based on minimum mean square deviation of potential energies. Stochastic Structural Dynamics, 1, (1991), pp. 327–338. https://doi.org/10.1007/978-3-642-84531-4 17.

F. Casciati, L. Faravelli, and A. M. Hasofer. A new philosophy for stochastic equivalent linearization. Probabilistic Engineering Mechanics, 8, (3-4), (1993), pp. 179–185. https://doi.org/10.1016/0266-8920(93)90013-l.

N. D. Anh and W. Schiehlen. New criterion for Gaussian equivalent linearization. European Journal of Mechanics - A/Solids, 16, (6), (1997), pp. 1025–1039.

C. Proppe, H. J. Pradlwarter, and G. I. Schu¨eller. Equivalent linearization and Monte Carlo simulation in stochastic dynamics. Probabilistic Engineering Mechanics, 18, (1), (2003), pp. 1–15. https://doi.org/10.1016/s0266-8920(02)00037-1.

I. Elishakoff, L. Andriamasy, and M. Dolley. Application and extension of the stochastic linearization by Anh and Di Paola. Acta Mechanica, 204, (1-2), (2009), pp. 89–98. https://doi.org/10.1007/s00707-008-0014-x.

R. N. Iyengar. Higher order linearization in non-linear random vibration. International Journal of Non-Linear Mechanics, 23, (5-6), (1988), pp. 385–391. https://doi.org/10.1016/0020-7462(88)90036-4.

N. D. Anh and M. Di Paola. Some extensions of Gaussian equivalent linearization. In Proceedings of International Conferenceon Nonlinear Stochastic Dynamics, Hanoi, Vietnam, (1995). pp. 5–16.

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, 268, (1), (2003), pp. 177–200. https://doi.org/10.1016/s0022-460x(03)00246-3.

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, 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, 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.

J. B. Roberts and P. D. Spanos. Random vibration and statistical linearization. Wiley, New York, (1990).

J. B. Roberts. A stochastic-theory for non-linear ship rolling in irregular seas. Journal of Ship Research, 26, (4), (1982), pp. 229–245.

J. B. Roberts and N. M. C. Dacunha. Roll motion of a ship in random beam waves: Comparison between theory and experiment. Journal of Ship Research, 29, (1985), pp. 112–126.

D. C. Polidori, J. L. Beck, and C. Papadimitriou. A new stationary PDF approximation for non-linear oscillators. International Journal of Non-Linear Mechanics, 35, (4), (2000), pp. 657–673. https://doi.org/10.1016/s0020-7462(99)00048-7.

C. W. S. To. Nonlinear random vibration: Analytical techniques and applications. CRC Press, (2011).




DOI: https://doi.org/10.15625/0866-7136/12015

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