Dynamic Behavior of Nonlinear Cable System. III
Publication: Journal of Engineering Mechanics
Volume 120, Issue 12
Abstract
The dynamic behavior of a geometrically nonlinear cable system is studied. Vector‐valued, nonwhite, correlated, stationary random excitation is used. The excitation has both additive and parametric components. The equations for the statistical moments of response are solved by numerical integration and by continuation. Simulation results are presented to assess the accuracy of the analytically predicted moments. The mean‐square response of the dominant coordinate decreases with increasing positive correlation between the excitation components. Increasing the prestrain of the system increases the linearized fundamental frequency and lowers responses. For some values of the parameters, the system has multiple stable and unstable mean‐square responses. Digital simulation shows that the system switches randomly in time from one stable branch to the other. The responses remain finite, so that the system can function safely in such regions. In general, the analytical predicted moments and those computed from simulation agree very well. Moreover, the multiple stable mean‐square responses predicted using Gaussian closure also match simulation results.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Arnold, L. (1974). Stochastic differential equations: theory and applications. John Wiley & Sons, New York, N.Y.
2.
Crandall, S. H. (1985). “Non‐Gaussian closure techniques for stationary random vibrations.” J. Nonlinear Mech., 20(1), 18.
3.
Doedel, E. (1986). AUTO: software for continuation and bifurcation problems in ordinary differential equations. CalTech, Pasadena, Calif.
4.
Gasparini, D. A., Perdikaris, P. C., and Kanj, N. (1989). “Dynamic and static behavior of cable dome model.” J. Struct. Engrg., ASCE, 115(2), 363–381.
5.
Georg, K., and Allgower, E. L. (1992). Numerical continuation methods. Springer‐Verlag, New York, N.Y.
6.
Ghiocel, D. M., and Gasparini, D. A. (1993). “Response of a cable system to vector‐valued random excitation.” 1993 Int. Conf. on Struct. Safety and Reliability (ICOS‐SAR), Innsbruck, Austria, 123–130.
7.
Ghiocel, D. M. (1993). “Nonlinear dynamic response of a cable system to additive and parametric random excitation,” PhD dissertation, Dept. of Civ. Engrg., Case Western Reserve Univ., Cleveland, Ohio.
8.
Gikhman, I. I., and Skorokhod, A. V. (1972). Stochastic differential equations. Springer‐Verlag, New York, N.Y.
9.
Lin, Y. K. (1967). Probabilistic theory of structural dynamics. McGraw‐Hill Book Co., Inc., New York, N.Y.
10.
Mesarovic, S., and Gasparini, D. A. (1992). “Dynamic behavior of nonlinear cable system I and II.” J. Engrg. Mech., ASCE, 118(5), 890–920.
11.
Rheinboldt, W. C. (1986). Numerical analysis of parametrized nonlinear equations. John Wiley & Sons, Inc., New York, N.Y.
12.
Schuss, Z. (1980). Theory and applications of stochastic differential equations. John Wiley & Sons, Inc., New York, N.Y.
13.
Seydel, R. (1988). From equilibrium to chaos: practical bifurcation and stability analysis. Elsevier, New York, N.Y.
14.
Soong, T. T. (1973). Random differential equations in science and engineering. Academic Press, Inc., San Diego, Calif.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jun 25, 1993
Published online: Dec 1, 1994
Published in print: Dec 1994
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.