Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities
نویسندگان
چکیده
منابع مشابه
Duffing equations with cubic and quintic nonlinearities
In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...
متن کاملAnalytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions
1 Departamento de Fı́sica, Ingenierı́a de Sistemas y Teorı́a de la Señal, Universidad de Alicante, Apartado 99, 03080 Alicante, Spain 2 Instituto Universitario de Fı́sica Aplicada a las Ciencias y las Tecnologı́as, Universidad de Alicante, Apartado 99, 03080 Alicante, Spain 3 Departamento de Ciencias Médicas, Facultad de Medicina, Universidad de Castilla-La Mancha, C/Almansa No. 14, 02006 Albacete, ...
متن کاملStability and Exact Multiplicity of Periodic Solutions of Duffing Equations with Cubic Nonlinearities
We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities, x + cx + ax − x = h(t), (∗) where a and c > 0 are positive constants and h(t) is a positive T -periodic function. We obtain sharp bounds for h such that (∗) has exactly three ordered T -periodic solutions. Moreover, when h is within these bounds, one of the three solutions is n...
متن کاملAn accurate closed-form approximate solution for the quintic Duffing oscillator equation
ABSTRACT An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method. In this method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude. The replacement of the origi...
متن کاملAnalytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation
In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which ...
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ژورنال
عنوان ژورنال: Nonlinear Dynamics
سال: 2016
ISSN: 0924-090X,1573-269X
DOI: 10.1007/s11071-016-2986-8