Numerical solution of Rayleigh equation in non-linear vibration

✍ Scribed by Chen, Y. Z. ;Lee, Kang Yong

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 60 KB
• Volume: 17
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/cnm.402

✦ Synopsis

Numerical solution of the Rayleigh equation in non-linear vibration is studied in this paper. The di erential equation is integrated on a particular interval (0; T p2 ) with the initial value condition, u = A i and du=dt = 0 at the time t = 0. The value T p2 is determined from the condition such that the trajectory of motion on the phase plane is a unclosed path around the original point with the both starting and the end point on the positive real axis. The target function method is developed to obtain the particular value T p2 . The obtained A i+1 (= u(T p2 )) will be used in the initial value condition of the next round integration. A stable periodic motion is obtained after some rounds of integration. The solution technique is out of the small parameter assumption in the Rayleigh equation. Finally, numerical examples and results are given.