Nonstationary Seismic Responses of Nonlinear Structural Systems to Modulated Earthquake Excitations
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
A simple structure under earthquake ground motion is modeled as single-degree-of-freedom systems with nonlinear or hysteretic stiffness subjected to modulated Gaussian white noise excitations. A nonstationary response is characterized in terms of probability density and statistical moments. According to the motion equation, a generalized Fokker-Planck-Kolmogorov (FPK) equation is derived. The exponential-polynomial closure (EPC) method, which is proposed previously for stationary solutions of the FPK equation, is further developed and extended by taking into account the time variable and generalized for nonstationary solutions. The solution is assumed as an exponential function of a series of polynomials with time-dependent unknown coefficients. With the Galerkin method, the time-dependent coefficients are then solved from the residual errors of a series of nonlinear differential equations. Thus, nonstationary probability densities and statistical moments are obtained. Finally, two types of nonlinear structural models, that is, structural systems with memory and without memory, under different modulating ground motions are considered. Typical modulating functions, that is, exponential type, box-car type, and Ang and Amin type are taken into account, and are assumed of the same Arias intensity. The proposed procedure is verified using Monte Carlo simulation. Moreover, the influences of the modulating function shape and Arias intensity on structure responses are discussed.
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Acknowledgments
This study was funded by the National Natural Science Foundation of China (Grant Nos. 11972273 and 51478382) and the National Natural Science Foundation of Shaanxi Province (Grant No. Z20180115).
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Oct 8, 2018
Accepted: Apr 10, 2019
Published online: Sep 28, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 28, 2020
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