Random Vibration under Propagating Excitation: Closed‐Form Solutions

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.