Active piezoelectric vibration control for a Timoshenko beam

Yildirim, Kenan; Küçük, İsmail

doi:10.1016/j.jfranklin.2015.10.019

Cited by 22 publications

(7 citation statements)

References 36 publications

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“…Due to this reason, nonlinear control of civil structures has attracted great attention [15]- [22]. Therefore, the present paper deals with the vibration control of a nonlinear system to show that the controlling of a nonlinear system is both possible and easy without linearization of the nonlinear system via the maximum principle [3]- [13].…”

Section: Introductionmentioning

confidence: 99%

A nonlinear plate control without linearization

Yildirim

Küçük

2017

Open Mathematics

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Abstract:In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

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Section: Introductionmentioning

confidence: 99%

A nonlinear plate control without linearization

Yildirim

Küçük

2017

Open Mathematics

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“…In [26], an integral-barrier Lyapunov function-based PDE control method is addressed for inhomogeneous Timoshenko beams with ensuring boundary output constraints. A piezoelectric vibration control scheme is considered for a Timoshenko beam with a minimum beam performance index function in [27]. However, researches in [23][24][25][26][27] all focus on the Timoshenko beam with a free end, which thus cannot represent the dynamics of the overhead crane bridge beam with a rigid trolley.…”

Section: Introductionmentioning

confidence: 99%

PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties

Liu

2020

IET Control Theory & Applications

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“…As the direct piezoelectric effect is usually utilized in engineering sensing and energy harvesters, the converse piezoelectric effect can be applied to structure control and active actuating. Kenan and Ismail studied the optimal piezoelectric vibration control of a Timoshenko beam [4] and Mindlin-type beam [5]. Shen et al [6] adopted piezoelectric elements to control the vibration of an autobody thin-wall structure by simplifying the thin-wall structure to a square plate with a peripheral clamped boundary.…”

Section: Introductionmentioning

confidence: 99%

Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

Fan

Min

2020

Materials

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Piezoelectric materials with the electro-mechanical coupling effect have been widely utilized in sensors, dampers, actuators, and so on. Engineering structures with piezoelectric actuators and sensors have provided great improvement in terms of vibration and noise reduction. The flexoelectric effect—which describes the coupling effect between the polarization gradient and strain, and between the strain gradient and electric polarization in solids—has a fourth-rank order tensor electro-mechanical coupling coefficient, and in principle makes the flexoelectricity existing in all insulating materials and promises an even wider application potential in vibration and noise control. In the presented work, a flexoelectric actuator was designed to actuate a simply supported beam. The electric field gradient was generated by an atomic force microscopy probe. Flexoelectric control force and moment components could be induced within the flexoelectric control layer. As flexoelectricity is size-dependent, the key parameters that could affect the actuating effect were examined in case studies. Analytical results showed that the induced flexoelectric control moment was strongly concentrated at the probe location. The controllable transverse displacement of the simply supported beam was calculated with the modal expansion method. It was found that the controllable transverse displacement was dependent on the probe location as well.

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Active piezoelectric vibration control for a Timoshenko beam

Cited by 22 publications

References 36 publications

A nonlinear plate control without linearization

A nonlinear plate control without linearization

PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties

Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

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