Probability Distribution of the Eigenvalues of the Random String Equation

[+] Author and Article Information
R. N. Iyengar, C. S. Manohar

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India

J. Appl. Mech 56(1), 202-207 (Mar 01, 1989) (6 pages) doi:10.1115/1.3176047 History: Received February 12, 1987; Revised May 24, 1988; Online July 21, 2009


The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Copyright © 1989 by ASME
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