• 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.

• Smart Structures and Systems
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• 제19권6호
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• pp.633-641
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• 2017

The complexity of macro-fiber composite (MFC) materials increasing the difficulty in simulation and analysis of MFC integrated structures. To give an accurate prediction of MFC bonded smart structures for the simulation of shape and vibration control, the paper develops a linear electro-mechanically coupled static and dynamic finite element (FE) models based on the first-order shear deformation (FOSD) hypothesis. Two different types of MFCs are modeled and analyzed, namely MFC-d31 and MFC-d33, in which the former one is dominated by the $d_{31}$ effect, while the latter one by the $d_{33}$ effect. The present model is first applied to an MFC-d33 bonded composite plate, and then is used to analyze both active shape and vibration control for MFC-d31/-d33 bonded plate with various piezoelectric fiber orientations.

• 대한기계학회논문집A
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• 제31권1호
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• pp.121-128
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• 2007

Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.

• 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.

• Smart Structures and Systems
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• 제10권2호
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• pp.111-130
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• 2012

Satellites with flexible lightweight solar panels are sensitive to vibration that is caused by internal actuators such as reaction or momentum wheels which are used to control the attitude of the satellite. Any infinitesimal amount of unbalance in the reaction wheels rotors will impose a harmonic excitation which may interact with the solar panels structure. Therefore, quenching the solar panel's vibration is of a practical importance. In the present work, the panels are modeled as laminated composite beam using first-order shear deformation laminated plate theory which accounts for rotational inertia as well as shear deformation effects. The vibration suppression is achieved by bonding patches of piezoelectric material with suitable dimensions at selected locations along the panel. These patches are actuated by driving control voltages. The governing equations for the system are formulated and the dynamic Green's functions are used to present an exact yet simple solution for the problem. A guide lines is proposed for determining the values of the driving voltage in order to suppress the induced vibration.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• Structural Engineering and Mechanics
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• 제31권5호
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• pp.481-506
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• 2009

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

• Composites Research
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• 제29권6호
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• pp.379-387
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• 2016

본 논문에서 전자기장과 열 하중을 받는 복합재료 평판에 대하여 압전재료를 이용한 압전제어를 수행하였다. 구조물에 가해지는 전자기장과 열 하중, 그리고 구성방정식에서 고려되는 압전효과가 모두 포함된 지배방정식을 FSDT 판 이론에 기초하여 Hamilton 원리에 의하여 유도하였다. 평판의 경계면에서 발생하는 제어력과 제어 모멘트는 비례제어 및 속도제어 로직에 의하여 적용되었다. 전자기장과 열 하중, 그리고 압전효과가 복합재료 평판의 동특성에 미치는 영향에 대하여 고찰하고, 압전효과 및 복합재료의 섬유각 변화를 통하여 복합재 구조물의 동특성을 효과적으로 제어 가능함을 확인하였다.

• Smart Structures and Systems
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• 제9권6호
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2001년도 추계학술발표대회 논문집
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• pp.191-194
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• 2001

A partially coupled thermo-piezoelectric-mechanical triangular finite element model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied mechanical 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. Nonconforming shape functions by Specht are employed in the transverse displacement variables. Numerical examples demonstrate the accuracy and efficiency of the proposed triangular plate element.