Global and Local Nonlinear System Responses under Narrowband Random Excitations. II: Prediction, Simulation, and Comparison
Publication: Journal of Engineering Mechanics
Volume 133, Issue 1
Abstract
The response behavior of the single-degree-of-freedom (SDOF) nonlinear structural system subjected to narrowband stochastic excitations studied in Part I is investigated via simulations to verify the stochastic system characteristics assumed in the development of the semianalytical method. In addition, to demonstrate the accuracy of the method, predicted response–amplitude probability distributions are presented and compared to simulation results. Numerical simulations are conducted by directly integrating the SDOF system with the narrowband excitation modeled by the 1971 Shinozuka formulation. It is observed that the proposed semianalytical method is capable of accurately characterizing the stochastic response behavior of the nonlinear system by predicting the response–amplitude probability distribution and capturing the trends of variations in the response–amplitude statistical properties. In both the primary and the subharmonic resonance regions, good agreements between the response–amplitude probability distributions predicted by the semianalytical method and obtained from simulation results are observed both qualitatively and quantitatively. In addition, trends of the variations in the probability masses associated with the modes with variations in excitation parameters (bandwidth and variance) are captured.
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Acknowledgments
Financial support from the U.S. Office of Naval Research (Grant Nos. ONRN00014-92-J-1221 and ONRN00014-04-10008) is gratefully acknowledged.
References
Davies, H. G., and Liu, Q. (1990). “The response envelope probability density function of a Dulling oscillator with random narrow-band excitation.” J. Sound Vib., 139, 1–8.
Davies, H. G., and Nandlall, D. (1986). “Phase plane for narrow-band random excitation of a duffing oscillator.” J. Sound Vib., 104, 277–283.
Davies, H. G., and Rajan, S. (1988). “Random superharmonic and subharmonic response: Multiple time scaling of a duffing oscillator.” J. Sound Vib., 26, 195–208.
Dimentberg, M. F. (1971). “Oscillations of a system with nonlinear cubic characteristics under narrow band random excitation.” Mech. Solids, 6, 142–146.
Dimentberg, M. F. (1988). Statistical dynamics of nonlinear and time-varying systems, Wiley, New York.
Francescutto, A. (1991). “On the probability of large amplitude rolling and capsizing as a consequence of bifurcations.” Proc., Int. Conf. on Offshore Mechanics and Arctic Engineering, Vol. II, 91–96.
Guckenheimer, J., and Holmes, P. (1986). Nonlinear oscillations, dynamical systems, and bifurcation of vector fields, Springer, New York.
Koliopulos, P. K., and Bishop, S. R. (1993). “Quasiharmonic analysis of the behavior of a hardening dulling oscillator subjected to filtered white noise.” Nonlinear Dyn., 4, 279–288.
Koliopulos, P. K., Bishop, S. R., and Stefanou, G. D. (1991). “Response statistics of nonlinear system under variations of excitation bandwidth.” Computational stochastic mechanics, Vol. 33, Elsevier Applied Science, London, 5–348.
Koliopulos, P. K., and Langley, R. S. (1993). “Improved stability analysis of the response of a duffing oscillator under filtered white noise.” Int. J. Non-Linear Mech., 28, 145–155.
Lin, H., and Yim, S. C. S. (1997). “Noisy nonlinear motions of moored systems. Part 1: Analysis and simulation.” J. Waterway, Port, Coastal, Ocean Eng., 123(5), 285–295.
Nayfeh, A. H., and Mook, D. T. (1979). Nonlinear oscillations, Wiley, New York.
Ochi, M. K. (1990). Applied probability and stochastic processes in engineering and physical sciences, Wiley, New York.
Rajan, S., and Davies, H. G. (1988). “Multiple time scaling of the response of a Duffing oscillator to narrow-band random excitation.” J. Sound Vib., 123, 497–506.
Roberts, J. B., and Spanos, P. D. (1986). “Stochastic averaging: An approximate method of solving random vibration problems.” Int. J. Non-Linear Mech., 21, 111–134.
Shinozuka, M. (1971). “Simulation of multivariate and multidimensional random processes.” J. Acoust. Soc. Am., 49, 357–367.
Shinozuka, M., and Deodatis, G. (1991). “Simulation of stochastic processes by spectral representation.” Appl. Mech. Rev., 44(4), 191–203.
Yim, S. C., Yuk, D., Naess, A., and Shih, I. M. (2007). “Global and local nonlinear system responses under narrowband random excitations, Part I: Semianalytical method.” J. Eng. Mech., 133(1), 22–29.
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© 2007 ASCE.
History
Received: Dec 19, 2005
Accepted: Apr 19, 2006
Published online: Jan 1, 2007
Published in print: Jan 2007
Notes
Note. Associate Editor: Ross Barry Corotis
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