Published in Proceedings of the 9th International Conference on Structural Safety and Reliability: Rome, Italy, June 1, 2005, pages 2177-2181. © 2005 ICCOSSAR 2005
NOTE: At the time of publication, the author William W. Durgin was not yet affiliated with Cal Poly.
In the present paper the eikonal equation is considered in the form of a second order, nonlinear ordinary differential equation with harmonic excitation due to internal wave. The harmonic excitation is taken imperfect, i.e. there is a random phase modulation due to Gaussian white noise. The amplitude and wavelength of the acoustic wave are used as the principle signal characteristics in bifurcation analysis. The regions of instability, identified using the bifurcation diagrams, examined through phase diagrams and Poincare maps. The effect of stochastic nature in addition to chaotic one of internal waves is demonstrated by means of comparison of the numerical data obtained for perfectly periodic excitation. Preliminary analysis shows very strong dependence on noise intensity at some values of amplitude and wave length of internal wave.