On the natural frequencies of a disordered linear chain of N degrees of freedom

Statistical properties of the natural frequencies of a linear chain having N degrees of freedom are derived assuming the physical properties of its elements or parameters are known only in a stochastic sense. The method of derivation is based upon a transfer matrix scheme together with a perturbation-type expansion. It is found that the top few natural frequencies have values which are very sensitive to the parameter variations whereas the lowest few are insensitive to these variations.