Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations

Jian, Peng; Xiang, Mingjiao; Li, Luxin; Sun, Hongxin; Wang, Xiuyong

doi:10.3390/app9081557

Cited by 17 publications

(7 citation statements)

References 58 publications

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“…Thus, for harder excitations, the system vibrates and delivers electrical output at smaller frequencies. This indicates that the subharmonic resonance regions are very sensitive to the excitation amplitude, which was also stated in Ref [45]. In addition, although the stable and unstable responses coexist in Fig.…”

Section: -Results and Discussionsupporting

confidence: 77%

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

2020

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This paper investigates the dynamical response of a nonlinear piezoelectric (PZT) energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in suband super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case.

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Section: -Results and Discussionsupporting

confidence: 77%

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

2020

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“…Because cables have the characteristics of light-weight, largeflexibility, and small-damping, those are used in civil engineering, navigation engineering, aerospace engineering, and other fields usually [1][2][3][4]. In civil engineering, from the investigation of long-span stay-cable bridges, it can find that large-scale vibration of stay-cables may occur under the loads of winds, rains, pedestrians, or vehicles [5][6][7]. In addition, the vibration characteristics of stay-cables are also affected by the tower column and bridge deck, which would make the dynamic behavior of stay-cables be more complex.…”

Section: Introductionmentioning

confidence: 99%

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Min

Liu

Wu³

et al. 2021

Discrete Dynamics in Nature and Society

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For the cable-bridge coupling model, the dynamic tension of cables is an important parameter to study the vibration characteristics of the model. Based on this concept, two calculation methods about dynamic tension of cables were introduced in great detail, and the influences of these two calculation methods on the vibration characteristics of cable-bridge coupling model were systematically investigated. Firstly, the vibration equation of the cable was derived based on the variational principle for Hamiltonian, and the vibration equation of the bridge deck was obtained by Newton’s law. Then, the vibration equation of the cable and bridge deck was transformed into ordinary differential vibration equation by the Galerkin method. In addition, the differences of the coefficients in the ordinary differential vibration equation obtained by these two calculation methods about dynamic tension were compared, and a parameter analysis was listed. Finally, the resonance mode of the cable-bridge coupling model was analyzed by a multiple scales method, and an example analysis was listed. The results of parameter analysis show that there are obvious differences in the linear coefficient and nonlinear coefficient of the ordinary differential vibration equation obtained by these two calculation methods. The results of example analysis show that, for the cable-bridge coupling model with 1 : 1 resonance, the amplitude of the model would not be different because of the two calculation methods about dynamic tension, but the amplitude of the cable would be affected by the calculation method significantly. It can be found that the research conclusions here can be helpful to the perfection of theoretical modeling and has certain guiding value for practical engineering.

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“…In (1.16) we are admitting that the delay is being considered in the longitudinal displacement of the beam, this seems to us very natural since there are several studies on piezoelectric structures considering the effect of delay on the mechanical part of the system [19,24,33,34].…”

Section: Introductionmentioning

confidence: 99%

Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights

Nonato,

Santos,

Raposo

2021

Preprint

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The main result of this work is to obtain the exponential decay of the solutions of a piezoelectric beam model with magnetic effect and delay term. The dampings are inserted into the equation of longitudinal displacement. The terms of damping, whose weight associated with them varies over time, are of the friction type, and one of them has delay. This work will also address the issue of existence and uniqueness of solution for the model.

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Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations

Cited by 17 publications

References 58 publications

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

Influences of Two Calculation Methods about Dynamic Tension on Vibration Characteristics of Cable-Bridge Coupling Model

Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights

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