Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory

Bendine, Kouider; Boukhoulda, Farouk Benallel; Nouari, Mohammed; Satla, Z.

doi:10.1007/s11803-016-0352-y

Cited by 27 publications

(12 citation statements)

References 23 publications

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“…Li et al [35] even proposed a model of functionally graded piezoelectric beam for its vibration analysis and revealed the increase of natural frequency and decrease of electric potential with increasing gradient index of the material. Recently, Bendine et al [36] studied the problem for active vibration control of functionally graded beams with upper and lower surface-bonded piezoelectric layers using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Khiem

Hai

Huong

2020

Mater. Res. Express

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The present paper addresses developing the Dynamic Stiffness Method (DSM) for natural frequency analysis of functionally graded beam with piezoelectric patch based on the Timoshenko beam theory and power law of material grading. Governing equations and general solution of free vibration are conducted for the beam element with piezoelectric layer that is modelled as a homogeneous Timoshenko beam. The obtained solution allows establishing dynamic stiffness matrix for modal analysis of FGM beam with bonded piezoelectric distributed sensors/actuators. Effect of thickness and position of the smart sensors/actuators and material parameters on natural frequencies is studied with the aim for dynamic testing and health monitoring of FGM structures. The theoretical developments are validated and illustrated by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Khiem

Hai

Huong

2020

Mater. Res. Express

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“…[6,7] introduced a new electromechanical model for plate with piezoelectric layers based on higher order shear deformation theory with the use of finite element method. More studies are provided by the research in the literature reader can refer to [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Optimal position of piezoelectric actuators for active vibration reduction of beams

Bendine

Polat

2020

Applied Mathematics and Nonlinear Sciences

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This paper investigates the optimal placement of piezoelectric actuators for the active vibration attenuation of beams. The governing equation of the beam is achieved by coupled first order shear deformation theory with two node element. The velocity feedback controller is designed and used to calculate the feedback gain and then apply to the beam. In order to search for the optimal placement of the piezoelectric actuators, a new optimization criterion is considered based on the use of genetic algorithm to reduce the displacement output of the beam. The proposed optimization technique has been tested for two boundary conditions configurations; clamped -free and clamped-clamped beam. Numerical examples have been provided to analyze the effectiveness of the proposed technic.

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“…The mesh free method based on element-free Galerkin method has been employed for active shape and vibration control of FGM plates using displacement field of FSDT and displacement-cum-velocity feedback (Dai et al 2005). Recently, active vibration control of Functionally graded beam with surface mounted layers of piezoelectric actuator and sensor is investigated using Reddy's third order shear deformation theory (TOT) and velocity feedback control algorithm (Bendine et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Finite element model based on an efficient layerwise theory for dynamics and active vibration control of smart functionally graded beams

Yasin

Prakash

Khan

2020

Mater. Res. Express

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In this work, we present a two-noded efficient finite element (FE) model incorporating the layer-wise mechanics for the dynamics and active vibration control of smart functionally graded (FG) beams. The material properties in the FG beam are assumed to vary smoothly in the thickness direction according to power law variation. The effective properties are computed using Mori-Tanaka homogenization scheme. Electric potential profile in the electroded piezoelectric layers/patches is assumed quadratic across its thickness. The equations of motion are derived using extended Hamilton's principle. Due to the complex algebraic expressions involved in the effective properties of FG system, the inertia and stiffness parameters are computed numerically using six point Gauss integration method. To fulfill the convergence requirements for weak integration of various energy terms in the variational formulation, the transverse displacement is interpolated with Hermite interpolation function possessing C 1 -continuity while the inplane displacement, shear rotation and quadratic component of the electric potential are interpolated with linear Lagrangian functions of C 0 -continuity. The equipotential condition of the electroded piezoelectric sensors and actuators is conveniently modelled using electric node concept. The control system is designed for constant gain velocity feedback (CGVF), and optimal LQR and LQG control strategies for a reduced order model using state space approach. The control performance is studied for single-input-single-output (SISO) and multi-input-multi-output (MIMO) configurations under various excitations. The effect of material inhomogeneity on stability/instability of the closed-loop response in the CGVF control has been discussed.

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Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory

Cited by 27 publications

References 23 publications

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Optimal position of piezoelectric actuators for active vibration reduction of beams

Finite element model based on an efficient layerwise theory for dynamics and active vibration control of smart functionally graded beams

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