Response of a Loaded Nonlinear String to Random Excitation

The response to white noise excitation of a light elastic string loaded at equal intervals by a number of equal masses is examined using the theory of the Markov random process and the associated Fokker-Planck equation. Taking nonlinear effects due to variation in string tension into account, an exact solution of the Fokker-Planck equation is obtained and used in an approximate analytical evaluation of the mean squared response of the system.