Dynamic and stability analysis of a cantilever beam system excited by a non-ideal induction motor

Jiang, Jiao; Kong, Xiangxi; Chen, Changzheng; Zhang, Zhaogang

doi:10.1007/s11012-021-01333-3

Cited by 10 publications

(4 citation statements)

References 28 publications

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“…2 shows the dynamic response flexible beam with rigid manipulator when sb = 0.5, ml = 0.2 and c = 0.15 N /s. Comparing with amplitude-frequency response curve without considering the effect of slope [12], the curve obtained by presented method exhibits spring softening behavior of the steady-state response. One can observe that the manipulator will eventually oscillate with a steady-state response corresponding to the excitation frequency (ω 1 ) since there is no trivial solution.…”

Section: A Primary Resonancementioning

confidence: 86%

“…where r is the scaling factor; q(t) is the time modulation, and ϕ(s) assumed as a linear combination of classical cantilever mode function which can been given by [12], [29]…”

Section: Equations Of Dynamicsmentioning

confidence: 99%

“…For example, the speed exclusion zone of a wind turbine, which was regarded as a typical cantilever beam structure attached with a rotating unbalanced mass, was investigated to prevent tower resonance [10]. The nonlinear dynamic behavior of a non-ideal unbalanced motor in a simple cantilever beam system was investigated and the results indicate there appears the jump phenomenon, namely the Sommerfeld effect [11], [12]. A model using RLC circuits with variable capacitance based on the saturation phenomenon is used to control the vibration of a hinged-hinged beam supporting unbalanced machine [13].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamics Analysis of a Large Flexible Slender Truss-Structure Carrying a Manipulator for On-Orbit Assembly

et al. 2022

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Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam-rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D'Alembert principle incorporated with the moment balance method where the beam is of a Euler-Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance (ω 1 ≈ ω ref ) and sub-harmonic resonance (ω 1 ≈ 2ω ref , ω 1 ≈ 3ω ref and ω 1 ≈ 4ω ref ) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.INDEX TERMS On-orbit assembly, flexible slender truss-structure mounted manipulator, parametric excitation, method of multiple scales, primary resonance, sub-harmonic resonance.

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Section: A Primary Resonancementioning

confidence: 86%

“…where r is the scaling factor; q(t) is the time modulation, and ϕ(s) assumed as a linear combination of classical cantilever mode function which can been given by [12], [29]…”

Section: Equations Of Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamics Analysis of a Large Flexible Slender Truss-Structure Carrying a Manipulator for On-Orbit Assembly

et al. 2022

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“…As an alternative to averaging, many researchers have exploited the method of Direct Separation of Motions [4] for the analysis of nonideally excited oscillators [9,21,24,39,41,42,49,50]. Of course, together with the analytical and numerical research, experimental studies are critical to understand nonideally excited oscillations.…”

Section: Actual Evolution Expected Evolution Natural Frequency Of The...mentioning

confidence: 99%

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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