Non-Stationary Response of a Non-Linear Cable Under Random Excitation


Abstract eng:
A cable is a typical structural component in the field of structure engineering. Under seismic loads, the cable performs random vibration. If the excitation intensity is considerably high, the cable vibrates with a non-linear large deflection. In such a case, the quadratic and cubic non-linear terms in displacement have to be considered and the response of the cable becomes complicated. This paper presents a study on non-stationary response of a non-linear cable under random excitation by a developed path integration method. In the path integration method, the Gauss-Legendre scheme and short-time Gaussian approximation are employed to numerically obtain the probability density function (PDF) of the cable. After that, the probability density evolution process is investigated in detail. Comparison with the exact stationary solution shows that the path integration method works well for approximating the PDF solution, even in the tail region. Due to the presence of the quadratic non-linear term in displacement, the PDF solution of displacement has a non-symmetric shape, which significantly differs from a Gaussian PDF distribution. The numerical analysis further shows that the initial PDF of displacement first shifts to the positive direction along displacement in the beginning and then it turns back around the stationary PDF distribution. For different time instants, the non-stationary PDFs differ significantly from each other. At a early time instant, the peak PDF corresponding to a larger displacement is much larger than the other peaks. This indicates that in the non-stationary state, a larger displacement has a much higher probability than the prediction of the stationary case. In a dynamical reliability analysis, the critical state possibly occurs in the non-stationary process. The non-stationary PDF behavior of velocity has a similar evolution to the one of displacement .This observation should be considered in the dynamical reliability analysis of a structure.

Contributors:
Conference Title:
Conference Title:
16th World Conference on Earthquake Engineering
Conference Venue:
Santiago (CL)
Conference Dates:
2017-01-09 / 2017-01-13
Rights:
Text je chráněný podle autorského zákona č. 121/2000 Sb.



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 Record created 2017-01-18, last modified 2017-01-18


Original version of the author's contribution as presented on USB, paper 3903.:
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