On the Stability and Long-Term Behaviour of Structural Systems Excited by Nonideal Power Sources

González-Carbajal, Javier; García-Vallejo, Daniel; Domı́nguez, J.

doi:10.1007/978-3-030-96603-4_12

Cited by 1 publication

(3 citation statements)

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“…We distinguish between the cases of large slope (d = O # (1)) and small slope (d = O # (ε))-symbol O # represents a sharp estimate, see Definition 1.4.4 in [38] or Definition 1.1.4 in [12]. While the case of large slope was investigated by the authors in [16][17][18], the case of small slope is the focus of the present work:…”

Section: Problem Statement and Assumptionsmentioning

confidence: 99%

“…Two different scenarios can be considered: 16) is exponentially attracted towards equilibrium (18) without approaching the resonance manifold. It can also be proved that, in this case, the outer averaged system is valid for all τ ∈ [0, ∞) (see Sect.…”

Section: Outer Regionmentioning

confidence: 99%

“…5.5 in [38]). 16) is also exponentially attracted towards fixed point (18). However, in its way towards the equilibrium, the considered trajectory will necessarily reach the neighbourhood of the resonance manifold, making system ( 16) no longer valid.…”

Section: Outer Regionmentioning

confidence: 99%

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Stability of a nonideally excited Duffing oscillator

2022

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This paper investigates the dynamics of a Duffing oscillator excited by an unbalanced motor. The interaction between motor and vibrating system is considered as nonideal, which means that the excitation provided by the motor can be influenced by the vibrating response, as is the case in general for real systems. This constitutes an important difference with respect to the classical (ideally excited) Duffing oscillator, where the amplitude and frequency of the external forcing are assumed to be known a priori. Starting from pre-resonant initial conditions, we investigate the phenomena of passage through resonance (the system evolves towards a post-resonant state after some transient near-resonant oscillations) and resonant capture (the system gets locked into a near-resonant stationary oscillation). The stability of stationary solutions is analytically studied in detail through averaging procedures, and the obtained results are confirmed by numerical simulations.

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Section: Problem Statement and Assumptionsmentioning

confidence: 99%

Section: Outer Regionmentioning

confidence: 99%