Improvement of a Krylov-Bogoliubov method that uses Jacobi elliptic functions
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Cited by (77)
An approximate method for solving force and displacement transmissibility of a geometrically nonlinear isolation system
2020, International Journal of Non-Linear MechanicsCitation Excerpt :Recently, IHBM was used for solving piecewise-linear piezoelectric energy harvester, which performed very effective and could be applied to further parameter optimization research [23]. Jacobi elliptic functions have been used to obtain the accurate results of the nonlinear equation of motion [24,25] by assuming the general solution of displacement response in the form of Jacobi elliptic functions [26–29]. Okabe et al. proposed a general elliptic averaging method for the nonlinear oscillators, which contain linear and cubic stiffness [30,31].
Exact analytical solutions for forced undamped Duffing oscillator
2016, International Journal of Non-Linear MechanicsAn analytical approach for predicting the energy capture and conversion by impulsively-excited bistable vibration energy harvesters
2016, Journal of Sound and VibrationForced response of low-frequency pendulum mechanism
2016, Mechanism and Machine TheoryCitation Excerpt :In the methods mentioned above, trigonometric approximations of the actual response are normally used. In the case of strongly nonlinear oscillators, qualitative improvement was observed when Jacobi elliptic functions instead of trigonometric functions are used for approximating the actual response and deriving approximate analytical solutions [7–11]. This observation suggests studying the response of such oscillators to a loading whose time course follows Jacobi elliptic functions, an idea that is taken up in the next section.
Reconstructing the transient, dissipative dynamics of a bistable Duffing oscillator with an enhanced averaging method and Jacobian elliptic functions
2016, International Journal of Non-Linear MechanicsJacobi elliptic functions: A review of nonlinear oscillatory application problems
2016, Journal of Sound and Vibration