Application of Jacobian Elliptic Functions to the Analysis of the Steady-State Solution of the Damped Duffing Equation with Driving Force of Elliptic Type
In this work, Jacobian elliptic functions are applied to obtain the approximate steady-state solution of the damped Duffing equation with driving force of elliptic type. We assume that the damping coefficient and the nonlinear term need not be small. Numerical comparison between the approximate solution and the numerical integration indicates that our proposed approximate steady-state solution captures well the amplitude-time vibrational response. We have also found that for a certain range of values of the driving frequency ω f and for a stiff spring, there are one, three, or five possible motions for the elliptic excitation amplitude-frequency response curve.
Keywordsdamped system elliptic integrals Floquet theory Jacobi elliptic functions nonlinear vibrations
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