Dynamics Response Control of a Mindlin-Type Beam

Yildirim, Kenan; Körpeoğlu, Seda Göktepe; Küçük, İsmail

doi:10.1142/s0219455417500390

Cited by 4 publications

(7 citation statements)

References 31 publications

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“…Mathematically, there are two parts in the braces in Equation (5). The first part is In Figure 5, it was found that the maximum value of the control moment increased sharply when decreasing the probe radius; in Figure 6, when increasing the flexoelectric patch thickness, the control moment increased.…”

Section: The Flexoelectric Control Momentmentioning

confidence: 99%

“…Mathematically, there are two parts in the braces in Equation (5). The first part is dependent on both the probe radius and patch thickness, and the second part is dependent on the probe radius only.…”

Section: The Flexoelectric Control Momentmentioning

confidence: 99%

“…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%

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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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Section: The Flexoelectric Control Momentmentioning

confidence: 99%

Section: The Flexoelectric Control Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

Fan

Min

2020

Materials

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“…Inspired by the work of Bernstein (1995) and Tyan and Bernstein (1995), the two types of controllers are combined through the performance index of piecewise function. The optimal nonlinear control law is then derived using Pontryagin's maximum principles (Yildirim, 2016; Yildirim and Kucuk, 2016; Yildirim et al., 2016).…”

Section: Optimally Saturated Nonlinear Constraint Control Lawmentioning

confidence: 99%

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

Liu

Ren

2017

Journal of Vibration and Control

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This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.

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“…The original contribution to literature is that the present paper is dealing with the vibration control by maximum principle of a Timoshenko beam, modeled as an equation including the derivatives of the state variable with respect to the time variable at the fourth order. The extended version of this work is to be published in [6].…”

Section: Introductionmentioning

confidence: 99%

Optimal Boundary Control of a Timoshenko Beam via Maximum Principle

Körpeoğlu¹,

Yildirim²,

Küçük³

2016

Modelling, Simulation and Identification / 841: Intelligent Systems and Control

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Boundary control to damp the undesirable vibrations in a Timoshenko beam is considered. For this purpose, controllability and wellposedness of the system are examined. Performance index is defined with regards to the dynamic response of the beam that is defined as a weighted quadratic functional of the displacement and the velocity at terminal time and expenditure of the control energy added as a penalty term. In order to obtain the optimal control function, an adjoint variable satisfying the adjoint equation corresponding to state equation is introduced. The maximum principle is formulated and optimal control function is obtained. Also, by using maximum principle, control problem is transformed into solving a system of partial differential equations including state and adjoint variables with initial, boundary and terminal conditions. MATLAB is used to obtain the solution of the system. Numerical results are given in tables and graphical forms.

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Dynamics Response Control of a Mindlin-Type Beam

Cited by 4 publications

References 31 publications

Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

Optimal Boundary Control of a Timoshenko Beam via Maximum Principle

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