Response of Nonclassically Damped MDOF Systems to Nonstationary Random Excitation

by E. A. Mashaly, Alexandria Univ, Egypt,
Ahsan Kareem, Alexandria Univ, Egypt,

Abstract: A procedure for calculating the dynamic response of a nonclassically damped multi-degree-of-freedom (MDOF) system to nonstationary non-white vector-valued random excitation is developed utilizing a modal time-domain approach. The nonstationary excitation is represented by an envelope-modulated stationary random process that may be expressed as a product of a stationary random process with a deterministic enveloped modulating function. The response of the coupled system is obtained at any time interval using the modal impulse-response function. The envelope intensity function is approximated by a staircase unit step function. This feature facilitates the use of envelope functions of any arbitrary shape. This formulation permits computations through a reduction in the multiplicity of the integrals involved in the evaluation of the response convariance matrices. The peak structural response values at any level on the structure are obtained by following the evolutionary distribution of the extreme values. The coupled lateral-torsional response of a ten-story unsymmetrical nonclassically damped building subjected to ground motion in any aribtrary direction is considered for illustrating the procedure developed here.

Subject Headings: Damping | Excitation (physics) | Building envelope | Ground motion | Stationary processes | Coupling | Equations of motion

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