期刊名称：Current Journal of Applied Science and Technology
印刷版ISSN：2457-1024
出版年度：2022
卷号：41
期号：25
页码：1-16
DOI：10.9734/cjast/2022/v41i2531771
语种：English
出版社：Sciencedomain International
摘要：Literature has shown that harmonically excited nonlinear Duffingand pendulum oscillators can respond chaotically under the influence of some of their drive parameters combination. However, literature is scarce on the steady state responses of these oscillators when excited arbitrarily and periodically. Therefore, thisresearch was designed to investigate the potential qualitative and quantitative variation in the steady Poincare solutions of nonlinear Duffing and pendulum oscillators under selected periodic excitations compared to their harmonically excited counterparts. The non-dimensional second Order Differential Equation (ODE) corresponding respectively to governing equations for harmonically/periodically excited nonlinear Duffing and pendulum were solved using the constant step fourth order Runge-Kutta algorithms. The corresponding steady state Poincare solutions obtained were characterised by visual inspection and fractal dimension measure obtained using fractal disk counting method. Visual inspection of corresponding steady Poincare solutions show that they are qualitatively indistinguishable. However, the corresponding estimated fractal dimension varied significantly. The absolute variation in dimension was found to be between 1.37% and 4.92% for the Duffing oscillator and between 5.67% and 7.39% for the pendulum oscillator.
关键词：Excited duffing oscillator;excited pendulum oscillator;fourth-order runge-kutta;fourier transformation;Periodic Excitation;poincare section and fractal disk characterisation
