Malaysian Journal of Mathematical Sciences, February 2016, Vol. 10(S)
Special Issue: The 3rd International Conference on Mathematical Applications in Engineering 2014 (ICMAE'14)
Solution of Cubic-Quintic Duffing Oscillators using Harmonic Balance Method
Hosen, M. A. and Chowdhury, M. S. H.
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
In this study, Harmonic Balance Method (HBM) is applied to determine approximate analytic solutions of strongly nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. Mainly, a set of nonlinear algebraic equations is solved in this method. The new method avoids the necessity of numerically solving sets of algebraic equations with very complex nonlinearities. Numerical comparisons between the HBM and the exact solutions reveal that the HBM is a promising tool for strongly nonlinear oscillator's problems.
Keywords: Approximate frequency, Harmonic balance method, Cubicquintic Duffing oscillator, Analytical solutions
