Random Response to Periodic Excitation with Correlated Disturbances
Publication: Journal of Engineering Mechanics
Volume 122, Issue 11
Abstract
The paper addresses non-Gaussian stationary response of linear single-degree-of-freedom (SDOF) systems subject to a periodic excitation with correlated random amplitude and phase disturbances that are modeled as correlated Gaussian white noise processes. Correlation between amplitude and phase modulation is specified by the cross-correlation coefficient. Numerical results for the second and fourth moment responses are presented. The probability density function of the response is calculated based on the cumulant-neglect closure method. Non-Gaussian nature of the response is discussed in terms of the excess factor. The results show that the moment responses generally increase with larger random amplitude disturbance and may decrease with larger random phase modulation for a lightly damped system at resonance. The cross correlation between amplitude and phase disturbances plays an important role in the system moment response. Larger system damping results in smaller system moment responses. The moment response may approach a limiting value, depending on the intensity of the amplitude disturbance, as the relative detuning or phase modulation increases. For the case of the phase modulation alone, the response may become Gaussian in the sense of up to the fourth-order moment for sufficiently large relative detuning or random phase disturbances.
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References
1.
Dimentberg, M. G. (1988). Statistical dynamics of nonlinear and time-varying system . Research Studies Press Ltd., Letchworth, England.
2.
Dimentberg, M. F. (1991). “A stochastic model of parametric excitation of a straight pipe due to slug flow of a two-phase fluid.”Proc., 5th Int. Conf. on Flow-Induced Vibrations, Brighton, England, 207–209.
3.
Dimentberg, M. F.(1992). “Stability and subcritical dynamics of structures with spatially disordered traveling parametric excitation.”Probabilistic Engrg. Mech., 7, 131–134.
4.
Dimentberg, M. F., Hou, Z. K., Noori, M. N., and Zhang, W. (1993). “Non-Gaussian response of a single-degree-of-freedom system to a periodic excitation with random phase modulation.”Recent development in the mechanics of continua (special volume). ASME, New York, N.Y.
5.
Grigoriu, M., Ruiz, S. E., and Rosenblueth, E.(1988). “Nonstationary models of seismic ground acceleration.”Earthquake Spectra, 4(3), 551–568.
6.
Hou, Z. K., Zhou, Y. S., Dimentberg, M. F., and Noori, M. (1994). “Non-stationary non-Gaussian response of linear SDOF system under randomly disordered periodic excitation.”Proc., Int. Conf. on Vibration Engrg., Beijing, China, 415–420.
7.
Hou, Z. K., Zhou, Y. S., Dimentberg, M. F., and Noori, M.(1995). “A non-stationary stochastic model for periodic excitation with random phase modulation.”Probabilistic Engrg. Mech., 10(1995), 73–81.
8.
Hou, Z. K., Zhou, Y. S., Dimentberg, M. F., and Noori, M. (1995). “A stationary model for periodic excitations with uncorrelated random disturbances.”Proc., 3rd Stochastic Struct. Dynamics Conf., San Juan, Puerto Rico, Jan. 15–18, 1995.
9.
Lin, Y. K., and Li, Q. C.(1993). “New stochastic theory for bridge stability in turbulent flow.”J. Engrg. Mech., ASCE, 119, 113–127.
10.
Longuet-Higgins, M. S. (1957). “The statistical analysis of a random, moving surface.”Philosophical Trans. Royal Soc., London, England, Ser. A(966), 321–387.
11.
Schueller, G. I., and Bucher, C. G. (1988). “Non-Gaussian response of systems under dynamic excitation.”Stochastic structural dynamics (progress in theory and applications), S. T. Ariaratnam, G. I. Schueller, and I. Elishakoff, eds., 219–239.
12.
Shinozuka, M., and Deodatis, G.(1988). “Stochastic process models for earthquake ground motion.”Probabilistic Engrg. Mech., 3(3), 114–123.
13.
Wedig, W. (1989). “Analysis and simulation of nonlinear stochastic systems.”Nonlinear Dynamics in Engineering Systems, W. Schiehlen, ed., Springer-Verlag KG, Berlin, Germany, 337–344.
14.
Wu, W. F., and Lin, Y. K.(1984). “Cumulant neglect closure for nonlinear oscillators under random parametric and external excitation.”Int. J. Non-linear Mech., 19, 349–362.
15.
Zeman, J. L.(1972). “Zur losung nichtlinearer stochastischer probleme der mechanik.”Acta Mechanica, 14, 157–169.
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Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 11 • November 1996
Pages: 1101 - 1108
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Nov 1, 1996
Published in print: Nov 1996
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