Wide-Band Random Axisymmetric Vibration of Cylindrical Shells

Analytical and numerical results are reported for the random vibrations of a uniform circular cylindrical shell excited by a ring load which is uniform around the circumference and random in time. The time history of loading is taken to be a stationary wide-band random process. The shell response is essentially one-dimensional but differs qualitatively and quantitatively from the response distributions for point-excited uniform strings and beams because of the large modal overlaps at the low end of the spectrum of shell natural frequencies. The contributions from the modal cross-correlations (which can usually be neglected for strings and beams) introduce an asymmetry into the distribution of mean-square response and can alter the magnitude of the local response considerably. For example, in a thin shell with a radius-to-length ratio of 0.5 the contribution to the mean-square velocity at the driven section due to the modal cross-correlations can be more than three times that due to the modal autocorrelations when the excitation is a band-limited white noise which includes 81 modes.