Coupled three-layered analysis of smart piezoelectric beams with different electric boundary conditions

Vasques, C. M. A.; Rodrigues, J. Dias

doi:10.1002/nme.1237

Cited by 34 publications

(19 citation statements)

References 29 publications

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“…It is now well known that since these theories do not account for the layerwise (zigzag) nature of distributions of the inplane displacements, they yield inaccurate results for moderately thick laminates and even thin laminates with strong inhomogeneity across the thickness. Vasques and Rodrigues [2005] presented a finite element formulation based on a coupled partial layerwise theory for three layer piezoelectric beams. Kapuria [2001] and Kapuria and Alam [2006] presented a coupled zigzag theory for hybrid beams, which considers a layerwise approximation for the inplane displacement, like the DLT, but the number of primary displacement variables is reduced to only three as in the ESL theories, FSDT and TOT, by enforcing the conditions on the transverse shear stresses at the top and bottom surfaces and the layer interfaces.…”

Section: Introductionmentioning

confidence: 99%

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Kapuria

Hagedorn

2007

JOMMS

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A unified coupled efficient layerwise theory is presented for the dynamics of smart laminated beams with surface-mounted and embedded piezoelectric actuators and sensors with arbitrary poling directions, acting in extension or shear mode. The theory considers a global third-order variation across the thickness combined with a layerwise linear variation for the axial displacement, expressed in terms of only three primary variables, and accounts for the transverse normal strain due to the electric field in the approximation for the transverse displacement. The electric potential is approximated as piecewise quadratic across sublayers. A finite element is developed which has two physical nodes with mechanical and some electric potential degrees of freedom (DOF), and an electric node for the electric potentials of the electroded surfaces of the piezoelectric patches. The electric nodes eliminate the need for imposition of equality constraints of the electric DOF on the equipotential electroded surfaces of the segmented piezoelectric elements and result in significant reduction in the number of electric DOF. The electric DOF associated with the physical nodes allow for the inplane electric field that is induced via a direct piezoelectric effect. The accuracy of the formulation is established by comparing the results with those available in literature and the 2D piezoelasticity solutions for extension and shear mode actuators, sensors and adaptive beams. The effect of segmentation of the electroded surface on the deflection, sensory potential and natural frequencies is illustrated for both extension and shear mode cases. The influence of the location of extension and shear mode actuators and sensors on the response is investigated for a hybrid mode composite beam. The effect of actuator thickness on the actuation authority is studied.

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Section: Introductionmentioning

confidence: 99%

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Kapuria

Hagedorn

2007

JOMMS

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“…Substituting into Equations (7) and (8) the induced electric fields in (6) and considering the strain definitions in (2), the electric field and potential become [11] …”

Section: Constitutive Equationsmentioning

confidence: 99%

“…The stiffness increase due to the induced electric fields expressed in Equation (22) is represented by the so-called effective stiffness parameters [11],c p(φ)…”

Section: Virtual Work Of the Internal Electromechanical Forcesmentioning

confidence: 99%

Finite Element Modelling of Beams with Arbitrary Active Constrained Layer Damping Treatments

Vasques¹,

Mace²,

Gardonio³

et al.

Civil-Comp Proceedings

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This paper concerns arbitrary active constrained layer damping (ACLD) treatments applied to beams. In order to suppress vibration, hybrid active-passive treatments composed of piezoelectric and viscoelastic layers are mounted on the substrate beam structure. These treatments combine the high capacity of passive viscoelastic materials to dissipate vibrational energy at high frequencies with the active capacity of piezoelectric materials at low frequencies. The aim of this research is the development of a generic analytical formulation that can describe these hybrid couplings in an accurate and consistent way. The analytical formulation considers a partial layerwise theory, with an arbitrary number of layers, both viscoelastic and piezoelectric, attached to both surfaces of the beam. A fully coupled electro-mechanical theory for modelling the piezoelectric layers is considered. The equations of motion, electric charge equilibrium and boundary conditions are presented. A one-dimensional finite element (FE) model is developed, with the nodal degrees of freedom being the axial and transverse displacements and the rotation of the centreline of the host beam, the rotations of the individual layers and the electric potentials of each piezoelectric layer. The damping behavior of the viscoelastic layers is modeled by the complex modulus approach. Three frequency response functions were measured experimentally and evaluated numerically: acceleration per unit force, acceleration per unit voltage into the piezoelectric actuator and induced voltage per unit force. The numerical results are presented and compared with experimental results to validate the FE model.

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“…Therefore, they lead to decoupled, partial and fully coupled electro-mechanical theories, which in turn can lead to different modifications of the structure's stiffness and different approximations of the physics of the system. These electro-mechanical coupling theories can be considered by the use of effective stiffness parameters, defined according the electric boundary condition considered, as shown by Vasques and Rodrigues [2] for a smart beam.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we start by succinctly describe the mathematical model utilized and a brief description of the one-dimensional FE developed by Vasques and Rodrigues [2] is presented. The kinematic and electric potential assumptions of the theoretical and FE spatial model are first presented.…”

Section: Introductionmentioning

confidence: 99%

Classical and Optimal Active Vibration Control of Smart Piezoelectric Beams

Vasques¹,

Rodrigues²

Civil-Comp Proceedings

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In this paper a numerical study concerning the active vibration control of smart piezoelectric beams is presented. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches with sensing and actuating capabilities.As a mathematical model, a one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized and briefly presented. The mathematical model considers a partial layerwise theory, with three discrete-layers, and a fully coupled electro-mechanical theory. The finite element model equations of motion and electric charge equilibrium are presented and recast into a state variable representation in terms of the physical modes of the beam.The analyzed case studies concern the vibration reduction of a cantilever aluminum beam with a pair of collocated piezoelectric patches mounted on the surface. The displacement time history, for an initial displacement field and white noise force disturbance, and point receptance at the free end are evaluated with the open-and closedloop classical and optimal control systems. The case studies allow to compare their performances and demonstrate their advantages and disadvantages.

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Coupled three-layered analysis of smart piezoelectric beams with different electric boundary conditions

Cited by 34 publications

References 29 publications

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Finite Element Modelling of Beams with Arbitrary Active Constrained Layer Damping Treatments

Classical and Optimal Active Vibration Control of Smart Piezoelectric Beams

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