Response of nonlinear oscillator under narrow-band random excitation. (English) Zbl 1123.70330


70L05 Random vibrations in mechanics of particles and systems
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[1] Den Hartog J P.Mechanical Vibrations[M]. Fourth edition. New York: McGraw-Hill, 1956. · Zbl 0071.39304
[2] Lyon R H, Heckl M, hazelgrove C B. Response of hard-spring oscillator to narrow-band excitation [J].Journal of the Acoustical Society of America, 1961,33(4): 1404–1411.
[3] Richard K, Anand G V. Nonlinear resonance in strings under narrow band random excitation-part I: planar response and stability[J].Journal of Sound and Vibration, 1983,86(8): 85–98. · Zbl 0507.73070
[4] Davies H G, Nandall D. Phase plane for narrow band random excitation of a Duffing oscillator[J].Journal of Sound and Vibration, 1986,104(2): 277–283. · Zbl 1235.70173
[5] Iyengar R N. Response of nonlinear systems to narrow-band excitation[J].Structural Safety, 1989,6(2): 177–185.
[6] Lennox W C, Kuak Y C. Narrow band excitation of a nonlinear oscillator[J].Journal of Applied Mechanics, 1976,43(2): 340–344. · Zbl 0352.70022
[7] Grigoriu M. Probabilistic analysis of response of Duffing oscillator to narrow band stationary Gaussian excitation[A]. In: E H Dowell Ed.Proceedings of First Pan-American Congress of Applied Mechanics[C]. Rio de Janeiro: Brazil, 1989.
[8] Davis H G, Liu Q. The response probability density function of a Duffing oscillator with random narrow band excitation[J].Journal of Sound and Vibration, 1990,139(1): 1–8. · Zbl 1235.70172
[9] Kapitaniak T. Stochastic response with bifurcations to non-linear Duffing’s oscillator[J].Journal of Sound and Vibration, 1985,102(3): 440–441.
[10] Fang T, Dowell E H. Numerical simulations of jump phenomena in stable Duffing systems[J].International Journal of Nonlinear Mechanics, 1987,22(2): 267–274.
[11] Zhu W Q, Lu M Q, Wu Q T. Stochastic jump and bifurcation of a Duffing oscillator under narrow-band excitation[J].Journal of Sound and Vibration, 1993,165(2): 285–304. · Zbl 0925.70303
[12] Wedig W V. Invariant measures and Lyapunov exponents for generalized parameter fluctuations [J].Structural Safety, 1990,8(1):13–25.
[13] Nayfeh A H.Introduction to Perturbation Techniques[M]. New York: Wiley, 1981. · Zbl 0449.34001
[14] Rajan S, Davies H G. Multiple time scaling of the response of a Duffing oscillator to narrow-band excitations[J].Journal of Sound and Vibration, 1988,123(3): 497–506. · Zbl 1235.70194
[15] Nayfeh A H, Serhan S J. Response statistics of nonlinear systems to combined deterministic and random excitations[J].International Journal of Nonlinear Mechanics, 1990,25(5): 493–509. · Zbl 0726.73045
[16] RONG Hai-wu, XU Wei, FANG Tong. Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation[J].Journal of Sound and Vibration, 1998,210(4): 483–515.
[17] ZHU Wei-qiu.Random Vibration[M]. Beijing: Science Press, 1992. (in Chinese)
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