Abstract
A statistical investigation of the effects of disorder on the dynamics of one-dimensional nearly periodic structures is presented. The problem of vibration propagation from a local source of excitation is considered. While for the ordered infinite system there exists a frequency passband for which the vibration propagates without attenuation, the introduction of disorder results in an exponential decay of the amplitude for all excitation frequencies. Analytical expressions for the localization factors (the exponential decay constants) are obtained in the two limiting cases of weak and strong internal coupling, and the degree of localization is shown to depend upon the disorder to coupling ratio and the excitation frequency. Both modal and wave propagation descriptions are used. The perturbation results are verified by Monte Carlo simulations. The phenomena of weak and strong localization are evidence. While the former affects little the dynamics of most engineering structures, the latter is shown to be of significant importance in structural dynamics.
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