Response of MDOF Systems to Vector Random Excitation

by Amitabha DebChaudhury, Asst. Prof.; Dept. of Materials Engrg., Univ. of Illinois at Chicago Circle, Chicago, Ill. 60680,
Dario A. Gasparini, Asst. Prof.; Dept. of Civ. Engrg., Case Western Reserve Univ., Cleveland, Ohio 44106,

Serial Information: Journal of the Engineering Mechanics Division, 1982, Vol. 108, Issue 2, Pg. 367-385

Document Type: Journal Paper


A model time history random vibration analysis is presented. The random excitation is nonwhite, nonstationary, vector-valued and correlated. Excitation components may have different frequency contents and variations in intensity with time. The correlation between any two components can be a function of time. The formulation is appropriate for any linear MDOF system which has been decoupled into modes. Analytical expressions are derived for the evolutionary mean and covariance matrices of a modal system augmented by filters and subjected to vector-valued excitation having piece-wise linear strength functions. Then, using modal superposition, evolutionary mean and covariance matrices of any response vector are computed. A three degree-of-freedom system, subjected to vector-valued earthquake excitation, is analyzed. The formulation captures the effects of nonstationarity and correlation between earthquake components.

Subject Headings: Excitation (physics) | Vector analysis | Correlation | Linear analysis | Matrix (mathematics) | Earthquakes | History | Vibration

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