This paper introduces a numerical technique for the estimation of stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise excitation. The Wiener-Hermite expansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variableorder damping. The numerical solver...

This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to inve...

To apply effective methods to analyze and distinguish all kinds of response patterns is an important issue of nonlinear dynamics. This paper contributes to develop an alternative Poincaré section method to analyze and identify the whirl responses of a nonlinear oscillator. This integration for analyzing high-order harmonic and chaotic motions is used to integrate the distance between state traj...

We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u′′ + g1(x)u ′ + g2(x)u + g3(x)u n + g4(x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing oscillator and numerous dynamical systems. The present work is an overview w...

The goal of this research is to improve the linearity of integrated oscillator based on switched-capacitor band-pass filter with a low Q-factor in order to achieve a feasible integration. With the minimum addition control digital control circuit, high linearity can be achieved by suppressing 3rd harmonic which requires high Q of filter in traditional way. Description. The aim of this research i...

the potential function of lippincott and schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. the parameters originally introduced to the potential function by lippincott and schroeder have been determined from the structural parameters such as 0.. .odistance 0-h bond distance, h.. .o distance and hoo angle. thevalidity of harmonic oscillator approxim...

The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is ...

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...