Analysis of a randomly excited non-linear stretched string

✍ Scribed by G. Tagata

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 583 KB
• Volume: 58
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(78)80063-7

✦ Synopsis

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 ofa 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.