The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) she...The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded(FG),the material properties vary along the thickness direction as one innovation of this study.Applying the first-order shear deformation theory(FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations(PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material(FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.展开更多
This article deals with the dynamic response analysis and active vibration control of the smart functionally graded material(FGM)composite core plate with FG piezoelectric material(FGPM)surface actuators and sensors.C...This article deals with the dynamic response analysis and active vibration control of the smart functionally graded material(FGM)composite core plate with FG piezoelectric material(FGPM)surface actuators and sensors.Considering a power law distribution,the mechanical and electrical material characteristics of the FGM and FGPM layers change continually along the thickness plane.The finite element method(FEM)and the first-order shear deformation theory(FSDT)are utilized in the modeling process for the FGM and FGPM layers.In the dynamic analysis,the dynamic response of the sandwich structure under the impact of sinusoidally distributed step load and the corresponding sensor voltage is obtained.To ensure that the simulations are accurate,the findings are compared with previously published research.To analyze the control efficiency of FGPM sensors and actuators on the FGM host structure,the linear quadratic regulator(LQR)controller is utilized.The sandwich structure is considered a multiple-input multiple-output system(MIMO),so sensors and actuators are placed at different locations on the plate surface.The modal strain energy method is utilized to find the appropriate location of the FGPM layers.According to the results of the analysis,it has been determined that piezoelectric material coefficients as well as mechanical properties are extremely important for obtaining optimum control performance from FGPM sensors and actuators.In addition,it is emphasized that active vibration control of FGM plates can be performed effectively with the proper selection of sensors and actuators and their accurate distribution on the plate.These results are expected to contribute to micro-electromechanical system(MEMS)sensor and actuator applications,soft robotics applications,and vibration protection and vibration damping applications of nanostructures.展开更多
Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material （FGPM） solid cylinder and sphere placed in a uniform magnetic field and subjected to the externa...Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material （FGPM） solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter β can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.展开更多
An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear ...An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.展开更多
In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the t...In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.展开更多
This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material （FGPM） and subjected to a uniform electric field and non-axisymmetric thermo-mechanical ...This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material （FGPM） and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson＇s ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.展开更多
Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM...Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.展开更多
A model of a piezoelectric structure with an inhomogeneous coating is considered.The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating.The properties of coa...A model of a piezoelectric structure with an inhomogeneous coating is considered.The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating.The properties of coating vary continuously in thickness from parameters of one material to parameters of another material in a continuously nonmonotonic or piecewise-continuous manner.As coating materials,various combinations of ceramics of different stiffness based on PZT are considered.Using the example of the problem of the propagation of sh-waves in a piezoelectric structure,we studied the influence of the ratio of the physical parameters of the coating materials,the localization region,and the size of the transition zone of one material to another on the propagation features of surface acoustic waves(SAWs)and the structure of the wave field.展开更多
Within the framework of the linearized theory of electroelastic wave propagation,a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a sy...Within the framework of the linearized theory of electroelastic wave propagation,a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered.The ferroelectric LiNbO_(3) is used as the main material of the structure.The initial deformed state of the coating material is homogeneous,induced by the action of initial mechanical stresses and an external electrostatic field,the properties of the coating continuously change in thickness.By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface,the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied.The separate and combined effects of initial actions on changes in the physical properties of the structure,the transformation of the surface wave field,and the change in the SAW velocities in a wide frequency range is studied.The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures,in the optimization and design of new structures and devices on SAW with high performance characteristics.展开更多
文摘The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded(FG),the material properties vary along the thickness direction as one innovation of this study.Applying the first-order shear deformation theory(FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations(PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material(FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.
文摘This article deals with the dynamic response analysis and active vibration control of the smart functionally graded material(FGM)composite core plate with FG piezoelectric material(FGPM)surface actuators and sensors.Considering a power law distribution,the mechanical and electrical material characteristics of the FGM and FGPM layers change continually along the thickness plane.The finite element method(FEM)and the first-order shear deformation theory(FSDT)are utilized in the modeling process for the FGM and FGPM layers.In the dynamic analysis,the dynamic response of the sandwich structure under the impact of sinusoidally distributed step load and the corresponding sensor voltage is obtained.To ensure that the simulations are accurate,the findings are compared with previously published research.To analyze the control efficiency of FGPM sensors and actuators on the FGM host structure,the linear quadratic regulator(LQR)controller is utilized.The sandwich structure is considered a multiple-input multiple-output system(MIMO),so sensors and actuators are placed at different locations on the plate surface.The modal strain energy method is utilized to find the appropriate location of the FGPM layers.According to the results of the analysis,it has been determined that piezoelectric material coefficients as well as mechanical properties are extremely important for obtaining optimum control performance from FGPM sensors and actuators.In addition,it is emphasized that active vibration control of FGM plates can be performed effectively with the proper selection of sensors and actuators and their accurate distribution on the plate.These results are expected to contribute to micro-electromechanical system(MEMS)sensor and actuator applications,soft robotics applications,and vibration protection and vibration damping applications of nanostructures.
基金The project supported by China postdoctoral science foundation(20060390260)Hunan Postdoctoral Scientific ProgramThe English text was polished by Yunming Chen.
文摘Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material （FGPM） solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter β can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.
基金supported by the University of Kashan(Nos.574613/01 and 574619/02)
文摘An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.
基金supported by the National Natural Science Foundation of China (Grants 11272040, 11322218)the Fundamental Research Funds for the Central Universities (Grant 2016YJS113)
文摘In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.
文摘This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material （FGPM） and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson＇s ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.
基金Project supported by the National Natural Science Foundation of China(No.11802319)the National Key Research and Development Program of China(No.2017YFB1102801)。
文摘Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.
基金This work was performed with a financial support of the Ministry of Science and Higher Education of the Russian Federation(project SSC-RAS N 01201354242)Russian Foundation of Basic Research(Grant No.19-08-01051).
文摘A model of a piezoelectric structure with an inhomogeneous coating is considered.The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating.The properties of coating vary continuously in thickness from parameters of one material to parameters of another material in a continuously nonmonotonic or piecewise-continuous manner.As coating materials,various combinations of ceramics of different stiffness based on PZT are considered.Using the example of the problem of the propagation of sh-waves in a piezoelectric structure,we studied the influence of the ratio of the physical parameters of the coating materials,the localization region,and the size of the transition zone of one material to another on the propagation features of surface acoustic waves(SAWs)and the structure of the wave field.
基金This work was performed with a financial support of the Ministry of Science and Higher Education of the Russian Federation(project 01201354242)Russian Foundation of Basic Research(projects 19-08-01051,19-01-00719).
文摘Within the framework of the linearized theory of electroelastic wave propagation,a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered.The ferroelectric LiNbO_(3) is used as the main material of the structure.The initial deformed state of the coating material is homogeneous,induced by the action of initial mechanical stresses and an external electrostatic field,the properties of the coating continuously change in thickness.By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface,the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied.The separate and combined effects of initial actions on changes in the physical properties of the structure,the transformation of the surface wave field,and the change in the SAW velocities in a wide frequency range is studied.The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures,in the optimization and design of new structures and devices on SAW with high performance characteristics.
