• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2013.10a
• /
• pp.206-213
• /
• 2013

Transient response of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar homogeneous piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layer vary continuously along the thickness. Laplace and Fourier transforms are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, and thickness of the layers. Computed results yield following conclusions: (a) the DERR increases with the increase of the gradient of the material properties of the FGPM layer; (b) certain direction and magnitude of the electric impact loading impedes crack extension; (c) increase of the thickness of the FGPM layer and the homogeneous piezoelectric layer which has larger material properties than those of the crack plane are beneficial to increase of the resistance of transient fracture of the FGPM layer.

• Smart Structures and Systems
• /
• v.16 no.5
• /
• pp.781-806
• /
• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• Advances in nano research
• /
• v.9 no.3
• /
• pp.193-210
• /
• 2020

In this research, beside presenting real images of produced Functionally Graded Carbon Nanotube-Reinforced Composites (FG-CNTRCs) and a brief review of the synthesis method of FG-CNTRCs, static and buckling analysis of FG-CNTRC with piezoelectric layers are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of Carbon Nanotubes (CNTs). To capture the size effects, nonlocal elasticity theory proposed by A.C. Eringen is also adopted in our model. One of the topics in our paper is using a higher order theory with eight different displacement fields and comparing their results with each other. To solve the governing equations, an analytical method is used to find the deflections and critical buckling loads of FG-CNTRCs. To show the accuracy of present methodology, our results are compared with the results of simply supported rectangular nano plates available in the literature. In this research, the effects of aspect ratio, piezoelectric layer and nonlocal parameter are also studied. It is hoped that this work leads to more accurate models on FG-CNTRC.

• Structural Engineering and Mechanics
• /
• v.34 no.4
• /
• pp.449-474
• /
• 2010

A smart hollow cylinder consisting of a host functionally graded elastic core layer and two surface homogeneous piezoelectric layers is presented in this paper. The bonding between the layers can be perfect or imperfect, depending on the parameters taken in the general linear spring-layer interface model. The effect of such weak interfaces on free vibration and steady-state response is then investigated. Piezoelectric layers at inner and outer surfaces are polarized axially or radially and act as a sensor and an actuator respectively. For a simply supported condition, the state equations with non-constant coefficients are obtained directly from the formulations of elasticity/piezoelasticity. An approximate laminated model is then introduced for the sake of solving the state equations conveniently. It is further assumed that the hollow cylinder is embedded in an elastic medium and is simultaneously filled with compressible fluid. The interaction between the structure and its surrounding media is taken into account. Numerical examples are finally given with discussions on the effect of some related parameters.

• Steel and Composite Structures
• /
• v.19 no.3
• /
• pp.713-733
• /
• 2015

In this paper, viscous fluid induced nonlinear free vibration and instability analysis of a functionally graded carbon nanotube-reinforced composite (CNTRC) cylindrical shell integrated with two uniformly distributed piezoelectric layers on the top and bottom surfaces of the cylindrical shell are presented. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC cylindrical shell are assumed to be graded through the thickness direction and are estimated through the rule of mixture. The elastic foundation is modeled by temperature-dependent orthotropic Pasternak medium. Considering coupling of mechanical and electrical fields, Mindlin shell theory and Hamilton's principle, the motion equations are derived. Nonlinear frequency and critical fluid velocity of sandwich structure are calculated based on differential quadrature method (DQM). The effects of different parameters such as distribution type of SWCNTs, volume fractions of SWCNTs, elastic medium and temperature gradient are discussed on the vibration and instability behavior of the sandwich structure. Results indicate that considering elastic foundation increases frequency and critical fluid velocity of system.

• Structural Engineering and Mechanics
• /
• v.67 no.1
• /
• pp.33-43
• /
• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.

• Steel and Composite Structures
• /
• v.38 no.3
• /
• pp.337-353
• /
• 2021

Micro-electro-mechanical systems (MEMS) are widely employed in sensors, biomedical devices, optic sectors, and micro-accelerometers. New reinforcement materials such as carbon nanotubes as well as graphene platelets provide stiffer structures with controllable mechanical specifications by changing the graphene platelet features. This paper deals with buckling analyses of functionally graded graphene platelets micro plates with two piezoelectric layers subjected to external applied voltage. Governing equations are based on Kirchhoff plate theory assumptions beside the modified couple stress theory to incorporate the micro scale influences. A uniform temperature change and external electric field are regarded along the micro plate thickness. Moreover, an external in-plane mechanical load is uniformly distributed along the micro plate edges. The Hamilton's principle is employed to extract the governing equations. The material properties of each composite layer reinforced with graphene platelets of the considered micro plate are evaluated by the Halpin-Tsai micromechanical model. The governing equations are solved by the Navier's approach for the case of simply-supported boundary condition. The effects of the external applied voltage, the material length scale parameter, the thickness of the piezoelectric layers, the side, the length and the weight fraction of the graphene platelets as well as the graphene platelets distribution pattern on the critical buckling temperature change and on the critical buckling in-plane load are investigated. The outcomes illustrate the reduction of the thermal buckling strength independent of the graphene platelets distribution pattern while meanwhile the mechanical buckling strength is promoted. Furthermore, a negative voltage, -50 Volt, strengthens the micro plate stability against the thermal buckling occurrence about 9% while a positive voltage, 50 Volt, decreases the critical buckling load about 9% independent of the graphene platelet distribution pattern.

• Structural Engineering and Mechanics
• /
• v.68 no.2
• /
• pp.203-213
• /
• 2018

This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.

• Smart Structures and Systems
• /
• v.23 no.3
• /
• pp.215-225
• /
• 2019

In the present paper, the nonlocal strain gradient refined model is used to study the thermal stability of sandwich nanoplates integrated with piezoelectric layers for the first time. The influence of Kerr elastic foundation is also studied. The present model incorporates two small-scale coefficients to examine the size-dependent thermal stability response. Elastic properties of nanoplate made of functionally graded materials (FGMs) are supposed to vary through the thickness direction and are estimated employing a modified power-law rule in which the porosity with even type of distribution is approximated. The governing differential equations of embedded sandwich piezoelectric porous nanoplates under hygrothermal loading are derived through Hamilton's principle where the Galerkin method is applied to solve the stability problem of the nanoplates with simply-supported edges. It is indicated that the thermal stability characteristics of the porous nanoplates are obviously influenced by the porosity volume fraction and material variation, nonlocal parameter, strain gradient parameter, geometry of the nanoplate, external voltage, temperature and humidity variations, and elastic foundation parameters.

• Steel and Composite Structures
• /
• v.20 no.3
• /
• pp.513-543
• /
• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.