Finite Difference Method for Computing Sound Propagation in Nonuniform Ducts

Abstract

Conclusion Compared to the rigorous procedures the solution to the previously stated problem, given by Eqs. (4) and (5) is approximate, but avoids the cumbersome calculations involved in the former. In this connection, the stochastic analysis of a single degree of freedom system subjected to random wind and seismic excitations to study the response characteristics was undertaken by the authors. The exciting force was assumed to be nonstationary in character, and was represented by the product of a deterministic shape function and a stationary random process characterized by its power spectral density. The choice of deterministic function and power spectral density was based on certain characteristics observed in a large number of past records of excitation process. The application of Eqs. (4) and (5) to study the peak response characteristics of the system revealed that the probability estimates for various appropriate values of X are about 0.5% below those obtained by an exact procedure.