Abstract
In the frequency region such that the non-linear terms arise from the fact that a string stretches in oscillation, when a narrow band random external force is applied, for a long period, to the string, it has been observed in digital simulation results that there is a small amplitude for which the amplitude probability density characteristic shows an anomalous “notchy” behaviour. This can be explained by the existence of a discontinuty in the amplitude resulting from the non-linear differential equation for a stretched string subjected to a random force, when analyzed by means of Stratonovich's quasi-static averaging method. In the Fokker-Planck equation obtained when one describes the stretched string by this non-linear differential equation with narrow band random forcing, the amplitude probability density characteristic is calculated by a polynomial approximation. The transition probability density function can be estimated by this method.
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