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Shape optimization of geometrically nonlinear modal coupling coefficients: an application to MEMS gyroscopes. [PDF]

Sci Rep
Schiwietz D, Hörsting M, Weig EM, Wenzel M, Degenfeld-Schonburg P.   +4 more
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Generalized trial equation method and its applications to Duffing and Poisson-Boltzmann equations

, 2017
Ali ÖZYAPICI
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Periodic Solutions of Duffing Equation

Periodic Solutions of Duffing Equation
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Periodically Forced Duffing's Equation

Journal of Sound and Vibration, 1994
Abstract Sufficient conditions are established for an equation of the type x ″ + α x + β x 3 = p ( t ) to have periodic solutions, where p ( t ) is periodic. The results are applied to analyze forced vibrations of a mass supported by a non-linear spring.
Mehri, B., Ghorashi, M.
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Quasiperiodic solutions of Duffing’s equations

Nonlinear Analysis: Theory, Methods & Applications, 1998
The existence of quasiperiodic solutions and the boundedness of all solutions to the equation \[ {d^2x \over dt^2}+ x^{2n+1} +\sum^l_{k=0} x^kp_k(t)=0,\;l\leq 2n, \] where \(p_0,\dots,p_l\) are quasi-periodic functions with frequencies \(\omega_1,\dots,\omega_m\), are considered. The Diophantine condition \(|k_1\omega_1+ \cdots+ k_m\omega_m|\geq c/ |k|^
Liu, Bin, You, Jiangong
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Integrable Duffing’s maps and solutions of the Duffing equation

Chaos, Solitons & Fractals, 2003
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Murakami, Wakako, Murakami, Chieko, Hirose, Kei-ichi, Ichikawa, Yoshi H.   +3 more
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Bifurcations and Chaos in Duffing Equation

Acta Mathematicae Applicatae Sinica, English Series, 2007
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Zhang, Meng, Yang, Jiangping
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FRACTIONAL DUFFING'S EQUATION AND GEOMETRICAL RESONANCE

International Journal of Bifurcation and Chaos, 2013
We investigate the Fractional Duffing equation in the presence of nonharmonic external perturbations. We have applied the concept of Geometrical Resonance to this equation. We have obtained the conditions that should be satisfied by the external driving forces in order to produce high-amplitude periodic oscillations avoiding chaos.
Jiménez, S., González, J. A., Vázquez, L.   +2 more
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2π-Periodic solutions of Duffing's equation

USSR Computational Mathematics and Mathematical Physics, 1986
The common properties of different classes of \(2\pi\)-periodic solutions of Duffing's nonlinear differential equation are investigated analytically and numerically. Generating periodic solutions are examined. The basic properties of \(2\pi\)-periodic solutions are investigated using the nonlinear functional analysis method.
Galaktionova, O. O., Zlatoustov, V. A.
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