Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

Vatankhah, Ramin; Najafi, Ali; Salarieh, Hassan; Alasty, Aria

doi:10.1016/j.jmaa.2014.03.012

Cited by 23 publications

(15 citation statements)

References 27 publications

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“…The study of its control properties is recent. Indeed, the boundary stabilization was addressed in Vatankhah et al, the internal stabilization was analyzed in Guzmán, the exact boundary controllability was solved in Guzmán and Zhu,Vatankhah et al, and Zhang and Wang, and the exact boundary observability was studied in Edalatzadeh et al The purpose of this paper is to improve the boundary stabilization result in Vatankhah et al…”

Section: Introductionmentioning

confidence: 97%

Boundary stabilization of a microbeam model

Guzmán

2020

Math Methods in App Sciences

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In this paper, we study the boundary stabilization of the deflection of a clamped-free microbeam, which is modeled by a sixth-order hyperbolic equation. We design a boundary feedback control, simpler than the one designed in Vatankhah et al, 2 that forces the energy associated to the deflection to decay exponentially to zero as the time goes to infinity. The rate in which the energy exponentially decays is explicitly given. KEYWORDSboundary stabilization, exponential energy decay, hyperbolic equation, Lyapunov techniques, microbeam model MSC CLASSIFICATION 35B40; 35L35; 74K10; 93B52 Math Meth Appl Sci. 2020;43:5979-5984. wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 97%

Boundary stabilization of a microbeam model

Guzmán

2020

Math Methods in App Sciences

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“…There are a number of investigations on this topic available in the literature; see and the references therein. But most of the contributions in the area of the controllability of flexible structures are confined to one or two dimensional flexible structures, such as strings, beams, plates, and shells . There are only a few contributions concerning three dimensional elasticity in comparison to one or two dimensional flexible structures.…”

Section: Introductionmentioning

confidence: 99%

Boundary Stabilization of a Cosserat Elastic Body

Najafi

Alasty

Vatankhah

et al. 2017

Asian Journal of Control

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Boundary stabilization of vibrating three-dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme.

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“…In contrast, in boundary control algorithm, the system is considered as a Partial Di erential Equation (PDE) where the controller is applied onto the boundary of the system and can change the response by changing the boundary conditions of the system [17][18][19]. In this method, the boundary parameters are changed in such a way that the desirable behavior of the system is achieved eventually [20][21][22][23][24][25]. This method may have a variety of applications in industry since the system is actuated only by its boundary and the controller is used only by the measured data from the boundary.…”

Section: Introductionmentioning

confidence: 99%

Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

et al. 2017

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Abstract. One of the methods of force/moment exertion on micro beams is utilizing piezoelectric actuators. In this paper, considering the e ects of the piezoelectric actuator on asymptotic stability achievement, the boundary control problem for the vibration of a clamped-free micro-cantilever Timoshenko beam is addressed. To achieve this purpose, the dynamic equations of the beam actuated by a piezoelectric layer laminated on one side of the beam are extracted. The control law was implemented so that vibrations of the beam could be decayed. This control law was achieved based on feedback of time derivatives of boundary states of the beam. The obtained control was applied in the form of piezoelectric voltage. To illustrate the impact of the proposed controller on the micro beam, the niteelement method and Timoshenko beam element were used, and then simulation operation was performed. The simulation shows that not only does this control voltage reduce the vibration of the beam, but also the mathematical proofs proposed in this article are precise and implementable.

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Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

Cited by 23 publications

References 27 publications

Boundary stabilization of a microbeam model

Boundary stabilization of a microbeam model

Boundary Stabilization of a Cosserat Elastic Body

Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

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