Determination of Approximate Periods of Duffing-harmonic Oscillator

Abstract

We introduced an analytical technique based on harmonic balance method (HBM) to determine approximate periods of a nonlinear Duffing-harmonic oscillator. Generally, a set of nonlinear algebraic equations are appeared when HBM is formulated. Investing analytically of such kinds of algebraic equations are a tremendously difficult task and cumbersome. In the present study, the offered technique gives desired results and to avoid numerical complexity. It is remarkable important that a third-order approximate period gives excellent agreement compared with numerical solution. The method is mainly illustrated by strongly nonlinear Duffing-harmonic oscillator but it is also useful for many other nonlinear oscillating systems arising in nonlinear sciences and engineering. doi:10.14456/WJST.2015.46

Keywords

• Approximate periods
• harmonic balance method
• Duffing-harmonic oscillator
• Power series solutions
• Perturbation Method