Strong Nonlinear Oscillators by Livija Cveticanin

Author:Livija Cveticanin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.112)

and the vibration decreases.

5.The obtained values can be compared with those obtained for the Van der Pol oscillator with constant mass

(5.113)

Thus, the relation (5.92) gives the amplitude–time variation

(5.114)

and the steady state amplitude

(5.115)

which is independent on the initial displacement. For parameter values and the steady state amplitude (5.115) for the linear oscillator is as it is previously published by Nayfeh and Mook (1979), while for the pure cubic nonlinear one is The value, given by Mickens (2010), is Comparing the solution of (5.113) obtained numerically, applying the Runge Kutta procedure, with the approximate amplitude (5.115) it can be concluded that the suggested solution in the form of the Jacobi elliptic function gives the more accurate result than the approximate trigonometric solution.

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