• Smart Structures and Systems
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• v.5 no.5
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• pp.531-546
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• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Advanced Composite Materials
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• v.16 no.1
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• pp.63-81
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• 2007

Based on the Kirchhoff hypothesis of normal-remain-normal, the present work analyses piezoelectric laminated plates, wherein poled piezoelectric laminae are transversely isotropic and function as actuators. A quadric electric field is induced inside a piezoelectric lamina under a given applied voltage and mechanical bending. The governing equations for the piezoelectric laminated plate derived from the principle of virtual work in terms of the electric enthalpy have the same forms as those for a conventional composite laminated plate. We use rectangular sandwich plates of Al/PZT/Al and PZT/Al/PZT with four simply supported edges to demonstrate the prediction of the maximum bending stress in the PZT layer. The analytic solutions are verified by three-dimensional finite element analysis.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.747-769
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• 2020

This paper provides a semi-analytical approach to investigate the variations of 3D displacement components, electric potential, stresses, electric displacements and transverse vibration frequencies in laminated piezoelectric composite plates based on the scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA). The proposed approach can analyze the static and dynamic responses of multilayered piezoelectric plates with any number of laminae, various geometrical shapes, boundary conditions, thickness-to-length ratios and stacking sequences. Only a longitudinal surface of the plate is discretized into 2D elements, which helps to improve the computational efficiency. Comparing with plate theories and other numerical methods, only three displacement components and the electric potential are set as the basic unknown variables and can be represented analytically through the transverse direction. The whole derivation is built upon the three dimensional key equations of elasticity for the piezoelectric materials and no assumptions on the plate kinematics have been taken. By virtue of the equilibrium equations, the constitutive relations and the introduced set of scaled boundary coordinates, three-dimensional governing partial differential equations are converted into the second order ordinary differential matrix equation. Furthermore, aided by the introduced internal nodal force, a first order ordinary differential equation is obtained with its general solution in the form of a matrix exponent. To further improve the accuracy of the matrix exponent in the SBFEM, the PIA is employed to make sure any desired accuracy of the mechanical and electric variables. By virtue of the kinetic energy technique, the global mass matrix of the composite plates constituted by piezoelectric laminae is constructed for the first time based on the SBFEM. Finally, comparisons with the exact solutions and available results are made to confirm the accuracy and effectiveness of the developed methodology. What's more, the effect of boundary conditions, thickness-to-length ratios and stacking sequences of laminae on the distributions of natural frequencies, mechanical and electric fields in laminated piezoelectric composite plates is evaluated.

• Structural Monitoring and Maintenance
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• v.7 no.2
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• pp.85-107
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• 2020

Dynamic responses of porous piezoelectric and metal foam nano-size plates have been examined via a four variables plate formulation. Diverse pore dispersions named uniform, symmetric and asymmetric have been selected. The piezoelectric nano-size plate is subjected to an external electrical voltage. Nonlocal strain gradient theory (NSGT) which includes two scale factors has been utilized to provide size-dependent model of foam nanoplate. The presented plate formulation verifies the shear deformations impacts and it gives fewer number of field components compared to first-order plate model. Hamilton's principle has been utilized for deriving the governing equations. Achieved results by differential quadrature (DQ) method have been verified with those reported in previous studies. The influences of nonlocal factor, strain gradients, electrical voltage, dynamical load frequency and pore type on forced responses of metal and piezoelectric foam nano-size plates have been researched.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.426-431
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• 2000

A decoupled thermo-piezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.42-49
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• 2006

In this paper, an efficient piezoelectric passive damper is newly devised to suppress the multi-mode vibration of plates. To construct the passive damper, the piezoelectric materials are utilized as energy transformer, which can transform the mechanical energy to electrical energy. To dissipate the electrical energy transformed from mechanical energy, multiple resonant shunted piezoelectric circuits are applied. The dynamic governing equations of a coupled electro-mechanical piezoelectric with multiple piezoelectric patches and multiple resonant shunted circuits is derived and solved for the one edge clamped plate. The equations of motion of the piezoelectrics and shunted circuits as well as the plate are discretized by finite element method to estimate more exactly the effectiveness of the piezoelectric passive damper. The method to find the optimal location of a piezoelectric is presented to maximize effectiveness for desired modes. The electro-mechanical coupling term becomes important parameter to select the optimal location.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.881-886
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• 2003

Vibration control of plates with a passive electrical damper is presented in this paper. This electrical absorber, piezoelectric patches connected with a resistor and an inductor in series, is analogous to the damped mechanical vibration absorber. For estimating the effectiveness of piezoelectric absorber, the governing equations of motion are derived using a classical laminate plate theory and Hamilton principle. The developed theoretical analyses are validated experimentally for simply-supported aluminum plates in order to demonstrate the performance of passive electrical damper. The result shows that the vibration amplitude is reduced about 14dB for the targeted first vibration mode.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1345-1362
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• 2015

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. $1^{st}$ and $2^{nd}$ modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.232-237
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• 2000

Thermopiezoelastic snap-through phenomena of piezolaminated plates are numerically investigated by applying a cylindrical arc-length scheme to Newton-Raphson method. Based on the layerwise displacement theory and von-Karman strain-displacement relationships, nonlinear finite element formulations are derived for thermopiezoelastic composite plates. From the static and dynamic viewpoint, nonlinear thermopiezoelastic behavior and vibration characteristics are studied for symmetric and eccentric structural models with various piezoelectric actuation modes. Present results show the possibility to enhance the performance of thermal structures using piezoelectric actuators and report new phenomena, namely thermopiezoelastic snapping, induced by the excessive piezoelectric actuation in the active suppression of thermally buckled large deflection of piezolaminated plates.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.46-49
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• 2000

A decoupled thermo-~lezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.