Abstract
A dual criterion of equivalent linearization method is suggested. The mean-square responses of Duffing, Van der Pol and Lutes-Sarkani oscillators subjected to random excitation are considered. The obtained results are compared with the numerical calculations of original systems and approximate solutions obtained by three different methods including the conventional linearization technique, energy method and regulation linearization method. The results show that in those nonlinear systems the accuracy of the mean-square response is significantly improved by the proposed criterion.
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Caughey T.K.: Response of Van der Pol’s oscillator to random excitations. Trans. ASME J. Appl. Mech. 26(1), 345–348 (1956)
Caughey T.K.: Random excitation of a system with bilinear hysteresis. Trans. ASME J. Appl. Mech. 27(1), 649–652 (1960)
Roberts J.B., Spanos P.D.: Random Vibration and Statistical Linearization. Wiley, New York (1990)
Socha, L.: Linearization methods for stochastic dynamic system. Lecture Notes in Physics. Springer, Berlin (2008)
Proppe C., Pradlwarter H.J., Schüller G.I.: Equivalent linearization and Monte-Carlo simulation in stochastic dynamics. J. Probab. Eng. Mech. 18(1), 1–15 (2003)
Foster E.: Semi-linear random vibrations in discrete systems. Trans. ASME J. Appl. Mech. 35, 560–564 (1968)
Atalik T., Utku S.: Stochastic linearization of multi-degree-of-freedom nonlinear system. J. Earthq. Eng. Struct. Dyn. 4, 411–420 (1976)
Brückner A., Lin Y.K.: Generalization of the equivalent linearization method for the nonlinear random vibration problems. Int. J. Nonlinear Mech. 22(4), 227–235 (1987)
Socha L., Soong T.T.: Linearization in analysis of nonlinear stochastic systems. Appl. Mech. Rev. 44, 399–422 (1991)
Casciati F., Faravelli L.: A new philosophy for stochastic equivalent linearization. J. Probab. Eng. Mech. 8, 179–185 (1993)
Zhang, X.T., Elishakoff, I., Zhang, R.C.: A stochastic linearization technique based on minimum mean-square deviation of potential energies. In: Lin, Y.K., Elishakoff, I. Stochastic Structural Dynamics–New Theoretical Developments, pp. 327–338. Springer, Berlin (1990)
Anh, N.D., Di Paola, M.: Some extensions of Gaussian equivalent linearization. International Conference on Nonlinear Stochastic Dynamics, pp. 5–16. Hanoi, Vietnam (1995)
Anh N.D., Schiehlen W.: A technique for obtaining approximate solutions in Gaussian equivalent linearization. Comput. Methods Appl. Mech. Eng. 168, 113–119 (1999)
Anh N.D., Hung L.X.: An improved criterion of Gaussian equivalent linearization for analysis of nonlinear stochastic systems. J. Sound Vib. 268(1), 177–200 (2003)
Crandall S.H.: A half-century of stochastic equivalent linearization. Struct. Control Health Monit. 13, 27–40 (2006)
Elishakoff I., Andrimasy L., Dolley M.: Application and extension of the stochastic linearization by Anh and Di Paola. Acta Mech. 204, 89–98 (2009)
Anh N.D.: Duality in the analysis of responses to nonlinear systems. Vietnam J. Mech. VAST. 32(4), 263–266 (2010)
Lutes, L.D., Sarkani, S.: Random Vibration: Analysis of Structural and Mechanical Systems, pp. 423–424, 437–438. Elsevier, Amsterdam (2004)
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Anh, N.D., Hieu, N.N. & Linh, N.N. A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation. Acta Mech 223, 645–654 (2012). https://doi.org/10.1007/s00707-011-0582-z
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DOI: https://doi.org/10.1007/s00707-011-0582-z