A general solution of the Duffing equation. (English) Zbl 1121.70016

Summary: We describe an application of elliptic balance method to obtain a general solution of forced damped Duffing equation by assuming that the moduli of Jacobi elliptic functions are slowly varying as a function of time. From this solution, the maximum transient and steady-state amplitudes are determined for large nonlinearities and positive damping. The amplitude-time response curves obtained from our approximate solution are in good agreement with numerical solutions over the selected time interval.


70K40 Forced motions for nonlinear problems in mechanics
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