Harichandran, R. S. (1992). "Random vibration under propagating
excitation: Closed-form solutions." Journal of Engineering Mechanics,
ASCE, 118(3), 575-586.
Abstract
Closed-form solutions are presented for random vibration response
integrals arising in the analysis of multi-degree-of-freedom (MDOF)
systems to stationary nodal and/or support excitations. Any pair of
excitations must either be fully coherent (i.e., have identical
frequency distribution) or totally incoherent. Fully coherent
excitations may propagate with constant velocity, and have local
amplitude variation. Solutions are presented for the response spectral
moments under commonly used excitation spectra, including white noise,
band-limited white noise, rational spectra, and spectra that are
piecewise linear in log-log scale. These solutions provide complete
generalizations of existing solutions, can save a great deal of
computational effort in the random vibration analysis of large systems,
and avoid difficulties that may be encountered in numerical integration
when the integrands are highly oscillatory due to slow propagation
velocities. It should be noted, however, that the solutions presented
cannot be applied when the excitations are partially coherent.