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Journal of Applied Nonlinear Dynamics 4(1) (2015) 21--42 | DOI:10.5890/JAND.2015.03.003

Nikolaos I. Xiros; Ioannis T. Georgiou

School of Naval Architecture and Marine Engineering, University of New Orleans, Louisiana, USA

School of Naval Architecture and Marine Engineering, National Technical University of Athens, Greece

Consultant Scientist, Leidos, Inc., Reston, VA 20190, USA

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Abstract

The nonlinear analysis of a typical electrical oscillator coupled nonlinearly to a mechanical one, as encountered in mechatronics applications for sensing, actuation and energy harvesting, is approached by using a state-space decomposition inspired by Volterra theory representation. The equation of motion of the mechanical subsystem includes an electromagnetic force directly proportional to the electric current squared. The nonlinear coupled dynamics is investigated systematically by partitioning the coupled system state vector in such a way as to fully exploit the mechanical low-pass and the electrical band-pass intrinsic features of free dynamics. In particular, by employing the Hilbert Transform, a low-pass equivalent system is derived and verified by using standard perturbation analysis. Then, a typical case is investigated thoroughly by means of numerical simulation of the original coupled low and band-pass, real-state-variable system and the low-pass-equivalent, complex-state-variable derived one. The nonlinear model equations considered here pave the way for a systematic investigation of nonlinear feedback control options designed to operate mechatronic transducers in energy harvesting, sensing or actuation modes.

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