An accurate closed-form approximate solution for the quintic Duffing oscillator equation

An 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...

Analytical 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, ...

Efficient Solution of Nonlinear Duffing Oscillator

In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

An explicit approximate solution to the Duffing- harmonic oscillator by a cubication method

Analytical Approximate Solutions for the Helmholtz- Duffing Oscillator

In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM ...