Harichandran, R. S. (1993). "An efficient, adaptive algorithm for
large-scale random vibration analysis." Earthquake Engineering and
Structural Dynamics, 22(2), 151-165.
Abstract
An efficient, adaptive and robust algorithm is proposed to reduce the
cost of large-scale stationary and transient random vibration analysis
of structures excited by multiple partially correlated nodal and/or base
excitations. The cost saving is accomplished by computing integrals
selectively, and yet attempting to maintain a level of accuracy desired
by the analyst. Recently proposed closed-form solutions for fully
coherent propagating band-limited white noise excitation are used to
approximately rank the terms in the modal covariance matrix. Terms are
then evaluated starting from the most important one, and the
computations are terminated in such a way that the accuracy level
requested by the user is satisfied in an approximate sense. Two
variations of the algorithm are proposed: the first one is more robust
and is preferred, and is recommended when computing a relatively small
number (hundreds) of response quantities; the second one is more
efficient when computing a very large number (thousands) of response
quantities. Both variations are adaptive, and explicitly consider the
closeness, damping and participation of all modes, while the first
method also considers the mode shapes. The efficiency and accuracy of
the algorithm is investigated by using it to compute the stationary and
transient seismic response of the Golden Gate suspension bridge.