Analysis of vibration of pendulum arm under bursting oscillation excitation

Simo, Hervé; Domguia, U. Simo; Dutt, J.K.; Woafo, P.

doi:10.1007/s12043-018-1661-7

Cited by 22 publications

(5 citation statements)

References 26 publications

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“…With the help of the modified fast-slow decomposition analysis method, one can also analyze the mechanism of different bursting behaviors of high-dimensional system on different subplanes as well as the synchronization problems. In addition, as we know, bursting oscillations also have the other application scenarios, such as circuit parameter configurations [41,42], energy harvesting [43,44], spatiotemporal communications [45,46] and laser signal analysis [47,48]. In the future, the applications and control of the bursting patterns obtained in this paper will be investigated.…”

Section: Discussionmentioning

confidence: 79%

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Lyu,

Li,

Huang

et al. 2023

Phys. Scr.

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The study of bursting oscillations induced by frequency-domain multiscale effect is one of the key scientific issues in the theoretical analysis of circuit systems. In this paper, we explore the mechanism of the bursting oscillations of a van der Pol-Duffing-Jerk circuit oscillator with slow-changing parametric and external periodic excitations. Three typical bursting modes, namely, left-right symmetric “subHopf/fold limit cycle” bursting, origin symmetric “fold/fold limit cycle” bursting and origin symmetric “fold/subHopf/fold limit cycle” bursting, are presented. The slowly changing excitation is treated as a generalized state variable to analyze the influence on the critical manifolds of the equilibria and bifurcations. The critical conditions of fold and Hopf bifurcations are computed by using the bifurcation theory, and two typical bifurcation structures are obtained according to the position of different bifurcation curves. Based on the bifurcation analysis, we investigate the appearance and dynamicalal evolutions of the different bursting oscillations with the variation of the external excitation amplitude. It is pointed that not only the bifurcation structures but also the distance between the fold and Hopf bifurcation points can affect the bursting patterns. We find the directions of the trajectories and the bursting types are sensitive to the values of the external excitation amplitude. Furthermore, we reveal the mechanism of the bursting oscillations by overlapping the trajectories on (,x)-plane onto the corresponding bifurcation structures. Numerical simulations are also presented to prove the correctness of the theoretical analysis in our study.

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Section: Discussionmentioning

confidence: 79%

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Lyu,

Li,

Huang

et al. 2023

Phys. Scr.

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“…In general, the bursting patterns found in this model arise from losses in the asymptotic stability of equilibrium point between the rest and active states associated with the appearance of zero eigenvalue. Understanding the bursting oscillations pattern in the gyroscope oscillator could be useful in its application to microelectromechanical systems (MEMS) gyroscopes with multiple driving forces [44,45] where the phenomenon can be employed to achieve rapid movement and control [19]. These can readily be explored in control systems and devices such as: RF switches; a phase shifter for spacecraft communication; lab-on-a-chip microsensors for remote chemical detection; compact thermal control systems for pico-and nano-satellites and inertial sensors for spacecraft navigation, which are all products of MEMS technology [46].…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

“…This phenomenon can occur in dynamical systems whose variables evolve on two different time scales, and it has potential applications in physics [9,10], mechanics [11], biology [12,13], chemistry [14,15], neuroscience [5,6], information encoding and computation [16], and in engineering systems [17,18]. The potential use of bursting in order to achieve extremely rapid actuators was recently demonstrated [19] in electromechanical systems .…”

Section: Introductionmentioning

confidence: 99%

Novel bursting oscillations in a nonlinear gyroscope oscillator

et al. 2022

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We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The bursting patterns arise when either the frequency or amplitude of the excitation force is varied. They take the form of pulse-shaped explosions (PSEs) wherein periodic attractors of lower periodicity disappear due to the loss of asymptotic stability of the equilibrium point between resting and active states. The process involves the appearance of zero eigenvalues and the creation of new attractors of higher periodicity. Both point-cycle and cycle-cycle bursting is seen. It is accompanied by the birth of periodic attractors, ranging from period one to period four, depending on an integer n in the frequency of the parametric driving force. The dynamics of the oscillator is shown to exhibit a fold bifurcation related to critical escape transitions.

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“…An inductive proximity sensor is composed of a primary side transducer (located on the sensing surface) and an electronic measuring circuit, as shown in Figure 1. The primary transducer is actually made up of inductors and capacitors, which generate electromagnetic fields through the excitation oscillation current inside the sensor, thus forming an induction surface at the end face of the sensor [12,13]. When the approaching distance or motion information of the target metal object changes, the parameters of the primary side transducer will change, such as the quality factor and coil inductance.…”

Section: Operating Principle Of Inductive Proximity Sensormentioning

confidence: 99%

An Implementation Method for an Inductive Proximity Sensor with an Attenuation Coefficient of 1

Zhao¹,

Fang²,

Yang³

et al. 2020

Energies

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In order to achieve long-distance measurement, a bridge differential inductance detection circuit is employed; on this basis, an automatic zero adjustment technique for sensors using an integral–proportional-integral controller is proposed in this work to achieve consistent product production and efficient installation and debugging, and the mathematical model of the bridge differential inductance detection circuit is established to effectively design the controller parameters. Furthermore, an implementation method for an inductive proximity sensor with an attenuation coefficient of 1 is also proposed based on the bridge differential inductance detection circuit by querying the proximity distance table in the field-programmable gate array (FPGA) to detect multiple target metal objects at the same inductive distance. Simulation and experimental results show that the proposed method is correct and effective.

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Analysis of vibration of pendulum arm under bursting oscillation excitation

Cited by 22 publications

References 26 publications

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Novel bursting oscillations in a nonlinear gyroscope oscillator

An Implementation Method for an Inductive Proximity Sensor with an Attenuation Coefficient of 1

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