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References
Brückner, A. and Lin, Y.: Application of complex stochastic averaging to nonlinear random vibration problems. Int. J. Non-Linear Mech. 22, 237–250, 1987.
Brückner, A. and Lin, Y.: Generalization of the equivalent linearization method for nonlinear random vibration problems. Int. J. Non-Linear Mech. 22, 227–235, 1987.
Cai, G.: Non-linear systems of multiple degrees of freedom under both additive and multiplicative random excitation. J. Sound Vib. 278, 889–901, 2004.
Chang, R. and Young, G.: Methods and Gaussian criterion for statistical linearization of stochastic parametrically and externally excited nonlinear systems. Trans. ASME J. Appl. Mech. 56, 179–185, 1989.
Chang, R.: A practical technique for spectral analysis of nonlinear systems under stochastic parametric and external excitations. Trans. ASME J. Vib. Acoust. 113, 516–522, 1991.
Chang, R.: Non-Gaussian linearization method for stochastic parametrically and externally excited nonlinear systems. Trans. ASME J. Dyn. Syst. Meas. Control 114, 20–26, 1992.
Evlanov, L. and Konstantinov, V.: Systems with Random Parameters. Nauka, Moskwa, 1976 (in Russian).
Falsone, G.: Stochastic linearization for the response of MDOF systems under parametric Gaussian excitation. Int. J. Non-Linear Mech. 27, 1025–1037, 1992.
Falsone, G.: The true linearization coefficients for nonlinear systems under parametric white-noise excitations. Trans. ASME J. Appl. Mech. 74, 161–163, 2007.
Ibrahim, R.: Parametric Random Vibration. Research Studies Press, Letchworth United Kingdom, 1985.
Kazakov, I. and Maltchikov, S.: Analysis of Stochastic Systems in State Space. Nauka, Moskwa, 1975 (in Russian).
Kottalam, J., Lindberg, K., and West, B.: Statistical replacement for systems with delta-correlated fluctuations. J. Stat. Phys. 42, 979–1008, 1986.
Naprstek, J. and Fischer, O.: Spectral properties of a non-linear self-excited system with random perturbations of the parameters. Z. Angew. Math. Mech. 77, 241–242, 1997 S1.
Proppe, C.: Statistical Linearization of Dynamical Systems Under Parametric Poisson White Noise Excitation. VDI Verlag, Düsseldorf, 2000 (in German).
Sobiechowski, C. and Sperling, L.: An iterative statistical linearization methods for MDOF systems. In: EUROMECH – 2nd European Nonlinear Oscillation Conference, Prague, pp. 419–422, September 9–13, 1996.
Socha, L.: Probability density equivalent linearization and non-linearization techniques. Arch. Mech. 51, 487–507, 1999.
Socha, L.: Probability density statistical and equivalent linearization techniques. Int. J. System Sci. 33, 107–127, 2002.
Soize, C.: Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: Prediction and identification procedures. Probab. Eng. Mech. 10, 143–152, 1995.
Soize, C. and Le Fur, O.: Modal identification of weakly non-linear multidimensional dynamical systems using stochastic linearization method with random coefficients. Mech. Syst. Signal Process. 11, 37–49, 1997.
Sperling, L.: Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions. Acta Mechanica 59, 183–200, 1986.
Young, G. and Chang, R.: Prediction of the response of nonlinear oscillators under stochastic parametric and external excitations. Int. J. Non-Linear Mech. 22, 151–160, 1987.
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Socha, L. (2008). Linearization of Dynamic Systems with Stochastic Parametric Excitations. In: Linearization Methods for Stochastic Dynamic Systems. Lecture Notes in Physics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72997-6_8
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