The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelec...The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.展开更多
The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materi...The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields i展开更多
In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, th...In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, the solution to the problem containing a Volterra-type screw dislocation is obtained by using the Fourier transform. The problem is then reduced to a set of Cauchy singular integral equations by the distributed dislocation method. Finally, several examples are presented to show the effect of the electro-elastic coating on the reduction of the stress intensity factors at the crack tips.展开更多
The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed_form solutions of the constraint_strain and the constraint_electric_field of a transversely is...The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed_form solutions of the constraint_strain and the constraint_electric_field of a transversely isotropic spherical inclusion in an infinite non_piezoelectric matrix are obtained. The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given. The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.展开更多
The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields.The analytical solution i...The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields.The analytical solution is obtained.The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation.From the results obtained,it can be found that the electro-elastic field depends on the material constants of individual phases,the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity.In addition,the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones,are also studied in this paper.展开更多
We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric ...We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.展开更多
The fundamental shear horizontal(SH0)waves have been proved to be a very useful method for nondestructive testing due to their non-dispersive characteristics.Currently,although several methods have been proposed to ge...The fundamental shear horizontal(SH0)waves have been proved to be a very useful method for nondestructive testing due to their non-dispersive characteristics.Currently,although several methods have been proposed to generate SH0 waves,it is still a challenge to obtain pure SH0 wave mode efficiently.Herein,in this study,non-centrosymmetric YBa3(PO_(4))3(YBP)and YbBa3(PO_(4))3(YbBP)crystals with pure face-shear mode were grown via the traditional Czochralski pulling method at temperatures above 1800℃.High resolution X-ray diffraction was carried out to evaluate the crystalline quality.Results showed that the YBP and YbBP crystals were of good quality,with the full width at half-maxima being on the order of 42.500 and 52.300,respectively.Moreover,the full set of electro-elastic constants for the YBP and YbBP crystals were determined and collated using a combination of impedance and pulse-echo methods.The piezoelectric coefficient(d14)of the YBP and YbBP crystals were determined to be 10.6 pC/N and 11.4 pC/N,respectively,corresponding to the electromechanical coupling coefficient(k14)equal to 15.4%and 15.9%,exhibiting large and pure face-shear vibration mode.Collectively,these results indicate that the YBP and YbBP crystals are promising for acoustic wave sensing application.展开更多
Rare-earth calcium oxyborate crystals(RECa_(4)O(BO_(3))_(3),RECOB,RE:rare-earth elements)are a kind of multifunctional crystal materials.In this work,the temperature dependent behaviors of the electroelastic constants...Rare-earth calcium oxyborate crystals(RECa_(4)O(BO_(3))_(3),RECOB,RE:rare-earth elements)are a kind of multifunctional crystal materials.In this work,the temperature dependent behaviors of the electroelastic constants of NdCOB crystal were investigated over the temperature range of-80-200℃,and their temperature coefficients were evaluated.It is found that NdCOB crystal possesses minimal variation of relative dielectric permittivities(<3%).The temperature coefficient of frequency for ZY cut with width shear vibration mode is in the order of 0.07×10^(-4)/℃.The temperature coefficients of the elastic compliances are obtained to be in the range of-33.0×10^(-4)/℃-32.2×10^(-4)/℃.Particularly,the sand swere found to show low temperature coefficients of the elastic compliances,i.e.1.0×10^(-4)/℃and-0.4×10^(-4)/℃,respectively,indicating the existence of zero temperature coefficient of frequency crystal cut.Furthermore,the electromechanical coupling factors and piezoelectric coefficients as a function of temperature were studied.The electromechanical coupling factor kand piezoelectric coefficient dare determined to be~30.8%and~15.2 pC/N at room temperature,respectively.The large piezoelectric response and zero temperature coefficient of frequency indicate the potential usage of NdCOB crystal for piezoelectric frequency devices over a wide temperature range.展开更多
A new approach to determine all the electro-elastic constants of the piezoelectric crystals in class 4mm has been put forward. As an example, all the constants of Lithium Tetraborate (Li2B4O7) crystal have been measur...A new approach to determine all the electro-elastic constants of the piezoelectric crystals in class 4mm has been put forward. As an example, all the constants of Lithium Tetraborate (Li2B4O7) crystal have been measured by means of the approach.The outstanding advantage of the approach is that it only needs to employ in measurement three crystal plates differently oriented.展开更多
This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation.The piezoelectric layers are...This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation.The piezoelectric layers are actuated with external applied voltage.The nanocore is assumed in-homogeneous in which the material properties are changed continuously and gradually along radial direction.Third-order shear deformation theory is used for the description of kinematic relations and electric potential distribution is assumed as combination of a linear function along thickness direction to show applied voltage and a longitudinal distribution.Electro-elastic size-dependent constitutive relations are developed based on nonlocal elasticity theory and generalized Hooke’s law.The principle of virtual work is used to derive governing equations in terms of four functions along the axial and the radial directions and longitudinal electric potential function.The numerical results including radial and longitudinal displacements are presented in terms of basic input parameters of the integrated cylindrical nanoshell such as initial electric potential,small scale parameter,length to radius ratio and two parameters of foundation.It is concluded that both displacements are increased with an increase in small-scale parameter and a decrease in applied electric potential.展开更多
In this paper, the free vibration of magneto- electro-elastic （MEE） nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rect...In this paper, the free vibration of magneto- electro-elastic （MEE） nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectan gular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton＇s principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.展开更多
The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded mate...The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded material are exponential, the state equation of structural vibration which takes the displacement and stress of the structure as state variables is derived. The natural frequencies and modal shapes are calculated based on the general solutions of the state equation and boundary conditions given in this paper. The influence of the functionally graded exponential factor on the elastic displacement, electric, and magnetic fields of the structure are discussed by assuming a sandwich plate model with different stacking sequences.展开更多
To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are de-rived and expressed in five harmoni...To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are de-rived and expressed in five harmonic functions from the governing equations and the strict differ-ential operator theorem. On the basis of these general solutions, the fundamental solution of infi-nite magneto-electro-elastic solid are obtained with the method of trial-and-error. Finally, the boundary integral formulation is derived and the corresponding boundary element method program is implemented to perform two numerical calculations(a column under uni-axial tension, uniform electric displacement or uniform magnetic induction, an annular plate simply-supported on outer and inner surfaces under axial loads). The numerical results agree well with the analytical ones.展开更多
Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditiona...Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.展开更多
This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally g...This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally graded(MEE-FG)nanobeam subject to elastic boundary constraints(BCs).The magneto-electric boundary condition and the Maxwell equation are used to calculate the variation of electric and magnetic potentials along the thickness direction of the nanobeam.This study is innovative since it does not use the conventional boundary conditions.Rather,an elastic system of straight and torsion springs with controllable stiffness is used to support nanobeams’beginning and end positions,creating customizable BCs.The governing equations of motion of nanobeams are established by applying Hamilton’s principle and IGA is used to determine deflections and natural frequency values.Verification studies were performed to evaluate the convergence and accuracy of the proposed method.Aside from this,the impact of the input parameters on the static bending and free oscillation of the MEE-FG nanobeam is examined in detail.These findings could be valuable for analyzing and designing innovative structures constructed of functionally graded MEE materials.展开更多
基金supported by Hebei Provincial Natural Science Foundation of China (Grant No. A2011210033)Foundation of Hebei Education Department of China (Grant No. ZH2011116)Hebei Provincial Research Program for Higher Education and Teaching Reformof China (Grant No. 103024)
文摘The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.
基金supported by Hebei Provincial Natural Science Foundation of China (Grant No. A2011210033)Foundation of Hebei Provincial Education Department of China (Grant No. ZH2011116)Hebei Provincial Research Program for Higher Education and Teaching Reform of China (Grant No. 103024)
文摘The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields i
文摘In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, the solution to the problem containing a Volterra-type screw dislocation is obtained by using the Fourier transform. The problem is then reduced to a set of Cauchy singular integral equations by the distributed dislocation method. Finally, several examples are presented to show the effect of the electro-elastic coating on the reduction of the stress intensity factors at the crack tips.
文摘The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed_form solutions of the constraint_strain and the constraint_electric_field of a transversely isotropic spherical inclusion in an infinite non_piezoelectric matrix are obtained. The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given. The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.
基金The project supported by the National Natural Science Foundation of China (19872023)the Foundation of the Ministry of Education for trans-century outstanding scholars
文摘The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields.The analytical solution is obtained.The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation.From the results obtained,it can be found that the electro-elastic field depends on the material constants of individual phases,the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity.In addition,the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones,are also studied in this paper.
文摘We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.
基金supported by the Primary Research&Development Plan of Shandong Province(2019JZZY010313)the National Natural Science Foundation of China(51872165).
文摘The fundamental shear horizontal(SH0)waves have been proved to be a very useful method for nondestructive testing due to their non-dispersive characteristics.Currently,although several methods have been proposed to generate SH0 waves,it is still a challenge to obtain pure SH0 wave mode efficiently.Herein,in this study,non-centrosymmetric YBa3(PO_(4))3(YBP)and YbBa3(PO_(4))3(YbBP)crystals with pure face-shear mode were grown via the traditional Czochralski pulling method at temperatures above 1800℃.High resolution X-ray diffraction was carried out to evaluate the crystalline quality.Results showed that the YBP and YbBP crystals were of good quality,with the full width at half-maxima being on the order of 42.500 and 52.300,respectively.Moreover,the full set of electro-elastic constants for the YBP and YbBP crystals were determined and collated using a combination of impedance and pulse-echo methods.The piezoelectric coefficient(d14)of the YBP and YbBP crystals were determined to be 10.6 pC/N and 11.4 pC/N,respectively,corresponding to the electromechanical coupling coefficient(k14)equal to 15.4%and 15.9%,exhibiting large and pure face-shear vibration mode.Collectively,these results indicate that the YBP and YbBP crystals are promising for acoustic wave sensing application.
基金Project supported by the National Natural Science Foundation of China(51872165)the Primary Research&Development Plan of Shandong Province(2019JZZY010313)+1 种基金Shandong Provincial Natural Science Foundation(ZR2020KA003)the Shandong Province Innovative Talents Support Program(62350070311104)。
文摘Rare-earth calcium oxyborate crystals(RECa_(4)O(BO_(3))_(3),RECOB,RE:rare-earth elements)are a kind of multifunctional crystal materials.In this work,the temperature dependent behaviors of the electroelastic constants of NdCOB crystal were investigated over the temperature range of-80-200℃,and their temperature coefficients were evaluated.It is found that NdCOB crystal possesses minimal variation of relative dielectric permittivities(<3%).The temperature coefficient of frequency for ZY cut with width shear vibration mode is in the order of 0.07×10^(-4)/℃.The temperature coefficients of the elastic compliances are obtained to be in the range of-33.0×10^(-4)/℃-32.2×10^(-4)/℃.Particularly,the sand swere found to show low temperature coefficients of the elastic compliances,i.e.1.0×10^(-4)/℃and-0.4×10^(-4)/℃,respectively,indicating the existence of zero temperature coefficient of frequency crystal cut.Furthermore,the electromechanical coupling factors and piezoelectric coefficients as a function of temperature were studied.The electromechanical coupling factor kand piezoelectric coefficient dare determined to be~30.8%and~15.2 pC/N at room temperature,respectively.The large piezoelectric response and zero temperature coefficient of frequency indicate the potential usage of NdCOB crystal for piezoelectric frequency devices over a wide temperature range.
文摘A new approach to determine all the electro-elastic constants of the piezoelectric crystals in class 4mm has been put forward. As an example, all the constants of Lithium Tetraborate (Li2B4O7) crystal have been measured by means of the approach.The outstanding advantage of the approach is that it only needs to employ in measurement three crystal plates differently oriented.
基金supported by the Research team project of Nanning University(2018KYTD03)the Science and Technology Planning Project of Yongning Zone of Nanning(20180205A)Henan Province Doctor Startup Fund of China under Grant No.2012BZ01.
文摘This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation.The piezoelectric layers are actuated with external applied voltage.The nanocore is assumed in-homogeneous in which the material properties are changed continuously and gradually along radial direction.Third-order shear deformation theory is used for the description of kinematic relations and electric potential distribution is assumed as combination of a linear function along thickness direction to show applied voltage and a longitudinal distribution.Electro-elastic size-dependent constitutive relations are developed based on nonlocal elasticity theory and generalized Hooke’s law.The principle of virtual work is used to derive governing equations in terms of four functions along the axial and the radial directions and longitudinal electric potential function.The numerical results including radial and longitudinal displacements are presented in terms of basic input parameters of the integrated cylindrical nanoshell such as initial electric potential,small scale parameter,length to radius ratio and two parameters of foundation.It is concluded that both displacements are increased with an increase in small-scale parameter and a decrease in applied electric potential.
基金supported by the Australian Research Council (DP130104358)Fundamental Research Funds for the Central Universities under Grant number 2013JBM009+1 种基金Program for New Century Excellent Talents in University under Grant number NCET-13-0656Beijing Higher Education Young Elite Teacher Project under Grant number YETP0562
文摘In this paper, the free vibration of magneto- electro-elastic （MEE） nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectan gular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton＇s principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.
基金Project supported by the National Natural Science Foundation of China (No. 50575172).
文摘The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded material are exponential, the state equation of structural vibration which takes the displacement and stress of the structure as state variables is derived. The natural frequencies and modal shapes are calculated based on the general solutions of the state equation and boundary conditions given in this paper. The influence of the functionally graded exponential factor on the elastic displacement, electric, and magnetic fields of the structure are discussed by assuming a sandwich plate model with different stacking sequences.
文摘To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are de-rived and expressed in five harmonic functions from the governing equations and the strict differ-ential operator theorem. On the basis of these general solutions, the fundamental solution of infi-nite magneto-electro-elastic solid are obtained with the method of trial-and-error. Finally, the boundary integral formulation is derived and the corresponding boundary element method program is implemented to perform two numerical calculations(a column under uni-axial tension, uniform electric displacement or uniform magnetic induction, an annular plate simply-supported on outer and inner surfaces under axial loads). The numerical results agree well with the analytical ones.
文摘Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.
文摘This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally graded(MEE-FG)nanobeam subject to elastic boundary constraints(BCs).The magneto-electric boundary condition and the Maxwell equation are used to calculate the variation of electric and magnetic potentials along the thickness direction of the nanobeam.This study is innovative since it does not use the conventional boundary conditions.Rather,an elastic system of straight and torsion springs with controllable stiffness is used to support nanobeams’beginning and end positions,creating customizable BCs.The governing equations of motion of nanobeams are established by applying Hamilton’s principle and IGA is used to determine deflections and natural frequency values.Verification studies were performed to evaluate the convergence and accuracy of the proposed method.Aside from this,the impact of the input parameters on the static bending and free oscillation of the MEE-FG nanobeam is examined in detail.These findings could be valuable for analyzing and designing innovative structures constructed of functionally graded MEE materials.
