A Hamiltonian approach to model and analyse networks of nonlinear oscillators: Applications to gyroscopes and energy harvesters

Pramana

Visarath In¹  Pietro-Luciano Buono²  Antonio Palacios2³  Bernard Chan³ 

[1] Space and Naval Warfare Systems Center, Code 71730 53560 Hull Street, San Diego, CA 92152-5001, USA$$;Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St N, Oshawa, ON L1H 7K4, Canada$$;Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA$$

关键词: Gyroscopes;    energy harvesters;    synchronization;    Hamiltonian mechanics.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Over the past twelve years, ideas and methods from nonlinear dynamics system theory, in particular, group theoretical methods in bifurcation theory, have been used to study, design, and fabricate novel engineering technologies. For instance, the existence and stability of heteroclinic cycles in coupled bistable systems has been exploited to develop and deploy highly sensitive, lowpower, magnetic and electric field sensors. Also, patterns of behaviour in networks of oscillators with certain symmetry groups have been extensively studied and the results have been applied to conceptualize a multifrequency up/down converter, a channelizer to lock into incoming signals, and a microwave signal generator at the nanoscale. In this manuscript, a review of the most recent work on modelling and analysis of two seemingly different systems, an array of gyroscopes and an array of energy harvesters, is presented. Empirical values of operational parameters suggest that damping and external forcing occur at a lower scale compared to other parameters, so that the individual units can be treated as Hamiltonian systems. Casting the governing equations in Hamiltonian form leads to a common approach to study both arrays. More importantly, the approach yields analytical expressions for the onset of bifurcations to synchronized oscillations. The expressions are valid for arrays of any size and the ensuing synchronized oscillations are critical to enhance performance.

【 授权许可】

Unknown