{"title":"Cyclostationary Gaussian Linearization for Analyzing Nonlinear System Response under Sinusoidal Signal and White Noise Excitation","authors":"R. J. Chang","volume":101,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":761,"pagesEnd":769,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10001242","abstract":"
A cyclostationary Gaussian linearization method is
\r\nformulated for investigating the time average response of nonlinear
\r\nsystem under sinusoidal signal and white noise excitation. The
\r\nquantitative measure of cyclostationary mean, variance, spectrum of
\r\nmean amplitude, and mean power spectral density of noise are
\r\nanalyzed. The qualitative response behavior of stochastic jump and
\r\nbifurcation are investigated. The validity of the present approach in
\r\npredicting the quantitative and qualitative statistical responses is
\r\nsupported by utilizing Monte Carlo simulations. The present analysis
\r\nwithout imposing restrictive analytical conditions can be directly
\r\nderived by solving non-linear algebraic equations. The analytical
\r\nsolution gives reliable quantitative and qualitative prediction of mean
\r\nand noise response for the Duffing system subjected to both sinusoidal
\r\nsignal and white noise excitation.<\/p>\r\n","references":"[1] A. A. Pervozvanskii, Random Processes in Nonlinear Control Systems,\r\nNew York: Academic Press, 1965.\r\n[2] P. Jung, \u201cPeriodically driven stochastic systems,\u201d Physics Reports, vol.\r\n234, nos. 4, 5, pp. 175-295, 1993.\r\n[3] A. Jha and E. Nikolaidis, \u201cVibration of dynamic systems under\r\ncyclostationary excitations,\u201d AIAA J., vol. 38, no. 12, pp. 2284-2291,\r\n2000.\r\n[4] K. Ellermann, \u201cOn the determination of nonlinear response distributions\r\nfor oscillators with combined harmonic and random excitation,\u201d\r\nNonlinear Dynamics, vol. 42, pp. 305-318, 2005.\r\n[5] W. A. Gardner, N. Antonio, and P. Luigi \"Cyclostationarity: Half a\r\ncentury of research,\" Signal Processing, vol. 86, no. 4, pp. 639\u2013697,\r\n2006.\r\n[6] A. B. Budgor, \u201cStudies in nonlinear stochastic processes. III.\r\nApproximate solutions of nonlinear stochastic differential equations\r\nexcited by Gaussian noise and harmonic disturbances,\u201d J. Statistical\r\nPhysics, vol. 17, no. 1, pp. 21-44, 1977.\r\n[7] A. R. Bulsara, K. Lindenberg, and K. E. Shuler, \u201cSpectral analysis of a\r\nnonlinear oscillator driven by random and periodic forces. I. Linearized\r\ntheory,\u201d J. Statistical Physics, vol. 27, no. 4, pp. 789-796, 1982.\r\n[8] R. N. Yengar, \u201cA nonlinear system under combined periodic and random\r\nexcitation,\u201d J. Statistical Physics, vol. 44, no. 5\/6, pp. 907-920, 1986.\r\n[9] A. H. Nayfeh and S. J., Serhan, Response statistics of non-linear systems\r\nto combined deterministic and random excitations, Int. J. Non-Linear\r\nMechanics, vol. 25, no. 5, pp. 493-505, 1990.\r\n[10] U. V. Wagner, On double crater-like probability density functions of a\r\nduffing oscillator subjected to harmonic and stochastic excitations,\u201d\r\nNonlinear Dynamics, vol. 28, pp. 343-355, 2002.\r\n[11] H. Rong, G. Meng, X. Wang, Xu, W., and T. Fang, Response statistic of\r\nnon-linear oscillator to combined deterministic and random excitation,\u201d\r\nInt. J. Non-Linear Mechanics, vol. 39, pp. 871-878, 2004. [12] Z. L. Huang, W. Q. Zhu, Y. Suzuki, \u201cStochastic averaging of non-linear\r\noscillators under combined harmonic and white-noise excitations,\u201d J.\r\nSound and Vibration, vol. 238, no. 2, pp. 233-256, 2000.\r\n[13] Y. J. Wu and W. Q. Zhu, \u201cStochastic averaging of strongly nonlinear\r\noscillators under combined harmonic and wide-band noise excitations,\u201d J.\r\nVibration and Acoustics, vol.130, 051004, pp. 1-19, 2008.\r\n[14] Z. L. Huang and W. Q. Zhu, \u201cStochastic averaging of quasi-integrable\r\nHamiltonian systems under combined harmonic and white noise\r\nexcitations,\u201d Int. J. Non-Linear Mechanics, vol. 39, pp. 1421-1434, 2004.\r\n[15] J. Yu and Y. Lin, \u201cNumerical path integration of a nonlinear oscillator\r\nsubject to both sinusoidal and white noise excitations,\u201d 5th Int. Conf.\r\nStochastic Structural Dynamics; Advances in stochastic structural\r\ndynamics, Florida, USA, 2003, pp. 525-534.\r\n[16] W. Xu, Q. He, T. Fang, and H. Rong, \u201cStochastic bifurcation in Duffing\r\nsystem subjected to harmonic excitation and in presence of random noise,\u201d\r\nInt. J. Non-Linear Mechanics, vol. 39, pp. 1473-1479, 2004.\r\n[17] U. V. Wagner and Wedig, W. V. \u201cOn the calculation of stationary\r\nsolutions of multi-dimensional Fokker-Planck equations by orthogonal\r\nfunctions,\u201d Nonlinear Dynamics, vol. 21, pp. 289-306, 2000.\r\n[18] L. Socha, Linearization Methods for Stochastic Dynamic Systems, Berlin:\r\nSpringer, 2008.\r\n[19] R. J. Chang, \u201cTwo-stage optimal stochastic linearization in analyzing of\r\nnon-linear stochastic dynamic systems,\u201d Int. J. Non-Linear. Mechanics,\r\nvol. 58, pp. 295-304, 2014.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 101, 2015"}