FREE-VIBRATION ANALYSIS OF STOCHASTIC STRINGS

The free vibration of strings with randomly varying mass and stiffness is considered. The joint probability density functions of the eigenva lues and eigenfunctions are characterized in terms of the solution of a pair of stochastic non-linear initial value problems. Analytical sol utions of these equations based on the method of stochastic averaging are obtained. The effects of the mean and autocorrelation of the mass process are included in the analysis. Numerical results for the margin al probability density functions of eigenvalues and eigenfunctions are obtained and are found to compare well with Monte Carlo simulation re sults. The random eigenvalues, when normalized with respect to their c orresponding deterministic values, are observed to tend to become firs t order stochastically stationary with respect to the mode count.