The method of averaging applied to a damped, non-linear system under harmonic excitation

✍ Scribed by G.L. Anderson

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 305 KB
• Volume: 40
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(75)80242-2

✦ Synopsis

To provide a more suitable analysis of the harmonically excited motion of certain nonlinear systems, the method of slowly varying phase and amplitude is modified so as to account for the presence of a linear damping term in the non-linear differential equation of motion. In the application of the technique described here, the assumption of very small linear damping has been relaxed. Approximate expressions for the amplitude and phase of the motion near a state of internal resonance are derived, and the frequency-amplitude relation for stationary oscillations is determined. It is shown that, in the limit of very small linear damping, the frequency-amplitude relation reduces to one derived by the more familiar version of the method of averaging.