• Advanced Composite Materials
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• 제16권1호
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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.

• 대한기계학회논문집
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• 제17권1호
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• pp.90-100
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• 1993

본 연구에서는 압전 감지기/작동기를 이용한 복합적층판의 진동제어해석을 위 하여 판요소를 사용한 능률적인 유한요소코드 개발에 있다. 운동방정식은 고전 적층 판이론과 Hamilton의 법칙을 이용하여 유도하며 압전방정식으로부터 전기적-기계적 연 계를 고려한 감지식과 작동식을 구한다.각식들은 유한요소 보간함수에 의하여 절점 변위에 대한 행렬방정식으로 변환된다. 요소마다 하나의 전기적 자유도를 가진 4-절 점 12-자유도 판요소를 사용하여 효율적인 계산을 가능하게 하였다. 압전 감지기/작 동기를 도입함에 있어 하나의 전극에 대해 압전 감지기/작동기는 하나의 감지/작동전 압을 갖는다. 각 요소에 전극번호를 부가함으로써 다양한 형상의 전극을 쉽게 모델 링하였으며 전극의 특성도 충분히 고려하였다. 전기적 하중에 의한 압전보의 변형과 변형에 대한 감지전압에 대한 계산을 수행하여 기존의 연구와 비교함으로써 본 프로그 램의 타당성을 확인하였다. 나아가 여러가지 전극형상에 대한 복합재료 평판의 시간 영역과 주파수영역에서 응답을 계산하였다.

• 대한기계학회논문집A
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• 제30권4호
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• pp.409-419
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• 2006

The actuating performance of plate-type unimorph piezoelectric composite actuators having various stacking sequences was evaluated by three dimensional finite element analysis on the basis of thermal analogy model. Thermal residual stress distribution at each layer in an asymmetrically laminated plate with PZT ceramic layer and thermally induced dome height were predicted using classical laminated plate theory. Thermal analogy model was applied to a bimorph cantilever beam and LIPCA-C2 actuator in order to confirm its validity. Finite element analysis considering thermal residual deformation showed that the bending behavior of piezoelectric composite actuator subjected to electric loads was significantly different according to the stacking sequence, thickness of constituent PZT ceramic and boundary conditions. In particular, the increase of thickness of PZT ceramic led to the increase of the bending stiffness of piezoelectric composite actuator but it did not always lead to the decrease of actuation distance according to the stacking sequences of piezoelectric composite actuator. Therefore, it is noted that the actuating performance of unimorph piezoelectric composite actuator is rather affected by bending stiffness than actuation distance.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Structural Engineering and Mechanics
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• 제75권6호
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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.

• Steel and Composite Structures
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• 제53권1호
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• pp.1-27
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• 2024

This work presents the effectiveness of differential quadrature shape functions (i.e., Lagrange interpolation polynomial, Cardinal sine function, Delta Lagrange kernel and Regularized Shannon kernel) in the solution of nonlinear vibration of multilayers piezoelectric plates with nonlinear elastic support. A piezoelectric composite laminated plate is rested on nonlinear Winkler and Visco-Pasternak elastic foundations problems. Based on 3D elasticity theory and piezoelectricity, the governing equations of motion are derived. Differential quadrature methods based on four shape functions are presented as numerical techniques for solving this problem. The perturbation method is implemented to solve the obtained nonlinear eigenvalue problem. A MATLAB code is written for each technique for solving this problem and extract the numerical results. To validate these methods, the computed results are we compare with the previous exact results. In addition, parametric analyses are offered to investigate the influence of length to thickness ratio, elastic foundation parameters, various boundary conditions, and piezoelectric layers thickness on the natural frequencies and mode shapes. Consequently, it is discovered that the obtained results via the proposed schemes can be applied in structural health monitoring.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 1999년도 추계학술발표대회 논문집
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• pp.15-21
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• 1999

This study investigates the free and forced vibration characteristics of an annular piezoelectric motor stator constructed of two piezoelectric material layers and one stainless steel layer. The annular piezoelectric motor stator is subjected to a travelling load produced by piezo drive electrical voltage input to the two piezoelectric layers. The stator is modeled as an annular laminated plate based on the classical plate theory and the governing equations are derived via Hamilton's variational principle. Variation of the free vibration characteristics as a function of several design parameters has been studied and based on this result, the forced vibration responses to the input electricity of various frequencies and magnitudes are investigated. The obtained results will provide an important criterion, a priori, in the design of piezoelectric motors.

• Smart Structures and Systems
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• 제4권1호
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• pp.19-34
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• 2008

Nowadays developments in the field of laminated composite structures with piezoelectric have attracted significant attention of researchers due to their wide range of applications in engineering such as sensors, actuators, vibration suppression, shape control, noise attenuation and precision positioning. Due to large number of parameters associated with its manufacturing and fabrication, composite structures with piezoelectric display a considerable amount of uncertainty in their material properties. The present work investigates the effect of the uncertainty on the free vibration response of piezoelectric laminated composite plate. The lamina material properties have been modeled as independent random variables for accurate prediction of the system behavior. System equations have been derived using higher order shear deformation theory. A finite element method in conjunction with Monte Carlo simulation is employed to obtain the secondorder statistics of the natural frequencies. Typical results are presented for all edges simply supported piezoelectric laminated composite plates to show the influence of scattering in material properties on the second order statistics of the natural frequencies. The results have been compared with those available in literature.

• 한국소음진동공학회논문집
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• 제12권1호
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• pp.5-11
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• 2002

Active vibration control of intelligent laminated composite plates is performed experimental1y Laminated composite place is modeled by the system identification method. For the system identification process, the laminated composite place is excited by two piezoelectric actuators with PRBS signals. At the same time, the displacement of the laminated composite plate is measured by a gap sensor. From these excited PRBS signals and the measured displacement sequence, system parameters of the laminated composite plate are estimated using a recursive prediction error method. Model of the laminated composite plate with two piezoeletric actuators is assumed to be the form of ARMAX. From the estimated ARHMAX model, a state space equation of the observable canonical form is obtained. With this state space equation, a controller and an observer for active vibration control is designed using the optimal control method. Controller and observer are implemented on a digital system. Experiments on the vibration control are Performed with changing the outer layer fiber orientation of intelligent composite plates.

• Smart Structures and Systems
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• 제15권5호
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• pp.1177-1202
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• 2015

The present paper is concerned with the optimal control and/or design of symmetric and antisymmetric composite laminate with two piezoelectric layers bonded to the opposite surfaces of the laminate, and placed symmetrically with respect to the middle plane. For the optimal control problem, Liapunov-Bellman theory is used to minimize the dynamic response of the laminate. The dynamic response of the laminate comprises a weight sum of the control objective (the total vibrational energy) and a penalty functional including the control force. Simultaneously with the active control, thicknesses and the orientation angles of layers are taken as design variables to achieve optimum design. The formulation is based on various plate theories for various boundary conditions. Explicit solutions for the control function and controlled deflections are obtained in forms of double series. Numerical results are given to demonstrate the effectiveness of the proposed control and design mechanism, and to investigate the effects of various laminate parameters on the control and design process.