Internal resonance of a two-degree-of-freedom tuned bistable electromagnetic actuator

Zhang, Jingyu; Li, Xuefeng; Li, Renfu; Dai, Lu; Wang, Wei; Yang, Kai

doi:10.1016/j.chaos.2020.110612

Cited by 14 publications

(6 citation statements)

References 41 publications

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“…Similar to the 2:1 IR [39,42], there are two steady-state solutions when the second mode of the system is directly excited. The first case is an uncoupled solution (aU), where only the directly excited resonator vibrates linearly when the excitation frequency is not within the natural frequency range of the internal coupling.…”

Section: Dynamic Analysismentioning

confidence: 95%

Multi-channel mass sensing based on multiple internal resonances in three electrostatically coupled resonators

Zhao

Sun

Kacem

et al. 2023

Preprint

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Multiple internal resonances in three electrostatically coupled microbeams have been theoretically investigated and were utilized to multi-channel mass detection. The frequency ratio among the three electrostatically coupled resonators of different sizes can be tuned to satisfy the specific conditions for multiple internal resonances. A reduced order model considering quadratic nonlinearity and frequency commensurability is established, and solved by the method of multiple scales, and verified by the harmonic balance method combined with the asymptotic numerical method. The nonlinear dynamics involving pitchfork and saddle-node bifurcations were analyzed and utilized to detect single, dual, or even multiple masses simultaneously. The frequency shift of the bifurcation points or the amplitude shift of a specific operating frequency near the bifurcation point were introduced as an output sensitivity. And then, a multi-channel single output detection mechanism was proposed, in addition to a single mass detection, the proposed sensor enables dual or even multi-channel mass detections based on frequency and amplitude shifts of pitchfork and saddle-node bifurcation points of the coupled and uncoupled vibration states. Furthermore, the effects of driving and coupling voltages on the dynamic response of the system were obtained. This work not only proposes a new way for multi-channel mass detection, but also provides technical support for multi-channel detection of other signals.

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Section: Dynamic Analysismentioning

confidence: 95%

Multi-channel mass sensing based on multiple internal resonances in three electrostatically coupled resonators

Zhao

Sun

Kacem

et al. 2023

Preprint

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“…The radial magnetic field due to the Halbach array can be known from equation (6). The radial magnetic flux density is centro symmetric, and the magnetic flux density generated by the permanent magnet array at a fixed axial position is only related to the internal size and permanent magnet material.…”

Section: Nonlinear Magnetic Field Analysismentioning

confidence: 99%

“…EMLA is a highly nonlinear coupling system. And various nonlinear and time-varying disturbances directly act on EMLA due to it directly driving the load [5][6][7][8]. In addition, the change of actuator parameters also directly affects normal operation of the system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear electromagnetic force analysis and compensation control of electromagnetic linear actuator

Yu,

Tan,

Yan

et al. 2023

Phys. Scr.

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Nonlinear electromagnetic force is a common phenomenon in electromagnetic linear actuators (EMLA). This nonlinearity limits the application in high-precision control systems. For facilitating the controller design, the influencing factors of nonlinear electromagnetic force were analyzed, and the quadratic polynomial with unknown weights was designed to approximate the nonlinear relationship among electromagnetic force, excitation current and displacement. An adaptive integral robust control algorithm based on electromagnetic force compensation (AIRC-FC) was designed, which combined the adaptive control law of electromagnetic force nonlinear compensation, stable feedback and error signal continuous integral robust control. The tracking performance and the adaptability of the EMLA with and without compensation control were analyzed under different loads. The results show that AIRC-FC improve the tracking performance of the EMLA effectively, and maintain high control accuracy under different loads.

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“…The results revealed that the nonlinear phenomena such as modal saturation, bifurcations and hysteresis were presented. Zhang et al [19] explored the 2:1 internal in a two-degree-of-freedom tuned bistable electromagnetic actuator with the consideration of quadratic nonlinearity. The jumping, saturation and bifurcation phenomenon were discussed.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nie¹,

Gao²,

Wang³

et al. 2022

J. Stat. Mech.

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The nonlinear behaviors of the L-shaped beam structure based on 1:2 internal resonance are investigated. The governing equations considering quadratic and cubic nonlinearity of the L-shaped beam structure are verified by the transient dynamic analysis of the finite element model. The approximate analytical solution for this system is derived by the method of multiple scales, and verified by the numerical solution. The Jacobian matrix of the modulation equation is employed to determine the equilibrium stability of the vibration response. The effects of the excitation frequency, amplitude and cubic nonlinear terms on the nonlinear responses of the primary resonance of the first and second modes are discussed. The bifurcation diagram, spectrum, phase plane and Poincaré section are applied to investigate the nonlinear vibration response. The results reveal that many nonlinear phenomena are observed, such as double-jump, hysteresis, Hopf bifurcation, modal saturation, multiple solutions, multi-softening and so on. The influence of cubic nonlinear term on internal resonance response should be considered. The broadband characteristics of internal resonance system are broadened by the nonlinear softening and hardening in the frequency response curve. In the primary resonance of the second mode, the hardening region in the frequency response curve becomes the softening region with the increase of excitation amplitude. The double-jump phenomenon is found in this newly formed softening region, and up to five solutions are observed in this region, including three sink points and two saddle-nodes. The broadband characteristics of the system is of great benefit to the application of broadband piezoelectric vibration energy harvesting.

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Internal resonance of a two-degree-of-freedom tuned bistable electromagnetic actuator

Cited by 14 publications

References 41 publications

Multi-channel mass sensing based on multiple internal resonances in three electrostatically coupled resonators

Multi-channel mass sensing based on multiple internal resonances in three electrostatically coupled resonators

Nonlinear electromagnetic force analysis and compensation control of electromagnetic linear actuator

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

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