Abstract
We use a nonlinear transformation method to develop equivalent equations of motion of nonlinear homogeneous oscillatory systems with linear and nonlinear odd damping terms. We illustrate the applicability of our approach by using the equations of motion that arise in many engineering problems and compare their amplitude-time curves with those obtained by the numerical integration solutions of the original equations of motion.
Highlights
The dynamics response of some systems can be more precisely described when nonlinear damping terms are used to model their dynamics behaviors
The dynamic behavior of double-well oscillators in which a nonlinear damping term with a fractional exponent covers the gaps between viscous, dry friction, and turbulent damping phenomena has been used by Litak et al in [5] to study, by using the Melnikov criterion, the system global homoclinic bifurcation and its transition to chaos
We examine the application of our proposed nonlinear transformation approach to obtain approximate solutions of the damped oscillatory systems such as the damped cubicquintic Duffing equation, the damped general pendulum equation of motion, the damped rational-form elastic term oscillator, and the nonlinear damped cubic term oscillator
Summary
The dynamics response of some systems can be more precisely described when nonlinear damping terms are used to model their dynamics behaviors. The dynamic behavior of double-well oscillators in which a nonlinear damping term with a fractional exponent covers the gaps between viscous, dry friction, and turbulent damping phenomena has been used by Litak et al in [5] to study, by using the Melnikov criterion, the system global homoclinic bifurcation and its transition to chaos It is evident from the previously mentioned works and references cited therein that the global system dynamics behavior can be accurately described if one is able to identify the order of the nonlinear stiffness and the damping effects that agree with the experimental observations [6]. We examine the application of our proposed nonlinear transformation approach to obtain approximate solutions of the damped oscillatory systems such as the damped cubicquintic Duffing equation, the damped general pendulum equation of motion, the damped rational-form elastic term oscillator, and the nonlinear damped cubic term oscillator
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