A nonlinearly coupled mathematical model of an electro-magneto-mechanical system is studied via the multiple scale approach in order to investigate its weakly nonlinear dynamics and analytically predict its salient features. The obtained amplitude modulation equations up to the third order perturbation allow to analytically describe the mechanical and electrical responses in terms of frequency-response curves and stability scenarios. A critical threshold of Hopf bifurcation is detected and analyzed as a function of the main system parameters. The subsequent extension of the asymptotic scheme up to the fifth order proves to grasp also the post-critical behavior, providing with the accurate identification of the amplitude of the quasiperiodic responses characterizing the unstable region of the ordinary differential equations system.

High order asymptotic dynamics of a nonlinearly coupled electromechanical system / Settimi, Valeria; Romeo, Francesco. - In: JOURNAL OF SOUND AND VIBRATION. - ISSN 0022-460X. - 432:(2018), pp. 470-483. [10.1016/j.jsv.2018.06.046]

High order asymptotic dynamics of a nonlinearly coupled electromechanical system

Settimi, Valeria
;
Romeo, Francesco
2018

Abstract

A nonlinearly coupled mathematical model of an electro-magneto-mechanical system is studied via the multiple scale approach in order to investigate its weakly nonlinear dynamics and analytically predict its salient features. The obtained amplitude modulation equations up to the third order perturbation allow to analytically describe the mechanical and electrical responses in terms of frequency-response curves and stability scenarios. A critical threshold of Hopf bifurcation is detected and analyzed as a function of the main system parameters. The subsequent extension of the asymptotic scheme up to the fifth order proves to grasp also the post-critical behavior, providing with the accurate identification of the amplitude of the quasiperiodic responses characterizing the unstable region of the ordinary differential equations system.
2018
Electromechanical system; Multiple scale method; Post-critical behavior; Stability analysis; Condensed Matter Physics; Acoustics and Ultrasonics; Mechanics of Materials; Mechanical Engineering
01 Pubblicazione su rivista::01a Articolo in rivista
High order asymptotic dynamics of a nonlinearly coupled electromechanical system / Settimi, Valeria; Romeo, Francesco. - In: JOURNAL OF SOUND AND VIBRATION. - ISSN 0022-460X. - 432:(2018), pp. 470-483. [10.1016/j.jsv.2018.06.046]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1152281
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