A near-distance,nonlinear coupling relationship objectively exists between urbanization and the eco-environment.The issue of how to coordinate the relationship between them has become a global strategic and scientific...A near-distance,nonlinear coupling relationship objectively exists between urbanization and the eco-environment.The issue of how to coordinate the relationship between them has become a global strategic and scientific issue.This study reveals the nature,relationship and intensity of coupling between urbanization and the eco-environment from a theoretical perspective.Based on the strength of coupling,relationships can be characterized as having very-low,low,medium,high,very-high or full coupling intensity,which correspond to the categories of random coupling,indirect coupling,loose coupling,cooperative coupling,close coupling,and controlled coupling.Together,these make up an urbanization and eco-environment"coupling tower."This study also develops an urbanization and eco-environment coupling circle theory and generates 45 coupling graphs(including linear,exponential-curve,logarithmic-curve,double exponential-curve and S-curve graphs)per 10°of rotation of the coupling circle,with different graphs corresponding to different urban development stages and development models.Of the various coupling graphs,the S-curve graph is considered the optimum,as it reflects the best interactivity scenario between urbanization and the eco-environment.Using an S-curve coupling graph,and with the help of an SD model and based on the complex one-to-one,one-to-many,and many-to-many relationships between the variables,this study develops the Urbanization and Eco-environment Coupler(UEC).The UEC is composed of 11 regulating elements and 201 variables.If one variable changes,it changes the whole,affecting the structure,function and regulation of the entire coupler.The UEC includes three spatio-temporal scales:static regulation between multiple urbanization areas and eco-environment areas at the same time,dynamic regulation between the same urbanization area and eco-environment area at different times,and dynamic regulation between multiple urbanization areas and eco-environment areas at different times.Regulation gradually promotes evolution from low-level coupling to high-level coupling between urbanization and the eco-environment.展开更多
<div style="text-align:justify;"> Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important app...<div style="text-align:justify;"> Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail. </div>展开更多
Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library...Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.展开更多
Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp （n=Q, 5）, combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order po...Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp （n=Q, 5）, combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin-orbit coupling. Spin-orbit coupling is included in the post Hartree-Fock procedure, i.e., in the coupled- cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.展开更多
Planar Bragg reflector operating in the sub-terahertz wavelength installed at the upstream end of a sheet beam back- ward wave oscillator （BWO） is very promising to minimize the whole circuit structure and make it m...Planar Bragg reflector operating in the sub-terahertz wavelength installed at the upstream end of a sheet beam back- ward wave oscillator （BWO） is very promising to minimize the whole circuit structure and make it more compact. In this paper, a sub-terahertz wavelength （0.18-0.22 THz） tunable planar Bragg reflector is numerically analyzed by using multi-mode coupling theory （MCT）. The operating mode TE10 and dominant coupling mode TE01 are mainly considered in this theory. Reflection and transmission performance of the reflector are demonstrated in detail and the results, in excellent agreement with the theoretical analysis and simulation, are also presented in this paper. Self- and cross-coupling coefficients between these two modes are presented as well. The reflector behaviors with different Bragg dimensions are discussed and analyzed in the 0.16-0.22 THz range. The analysis in this paper can be of benefit to the design and fabrication of the whole BWO circuit.展开更多
A non-classical Kirchhoff plate model is developed for the dynamic analysis of microscale plates based on the modified couple stress theory in which an internal material length scale parameter is included. Unlike the ...A non-classical Kirchhoff plate model is developed for the dynamic analysis of microscale plates based on the modified couple stress theory in which an internal material length scale parameter is included. Unlike the classical Kirchhoff plate model, the newly developed model can capture the size effect of microscale plates. Two boundary value problems of rectangular micro- plates are solved and the size effect on the lowest two natural frequencies is investigated. It is shown that the natural frequencies of the microscale plates predicted by the current model are size-dependent when the plate thickness is comparable to the material length scale parameter.展开更多
Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam th...Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.展开更多
Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform...Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.展开更多
The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theor...The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.展开更多
The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory ...The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.展开更多
In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering...In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh–Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon reveals that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli–Euler beam and material isotropy.展开更多
A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and s...A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.展开更多
In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted in...In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.展开更多
The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introdu...The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.展开更多
This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric laye...This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.展开更多
An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam an...An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.展开更多
A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value p...A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.展开更多
For the superstructure fiber grating(SFG)consisting of fiber Bragg grating(FBG)and long-period fiber grating(LPFG),there exist three kinds of coupling:the contra-directional coupling between forward propagating core m...For the superstructure fiber grating(SFG)consisting of fiber Bragg grating(FBG)and long-period fiber grating(LPFG),there exist three kinds of coupling:the contra-directional coupling between forward propagating core mode and backward propagating core mode,the contra-directional coupling between core mode and cladding mode,and the co-directional coupling between core mode and cladding mode.By using the similarity transformation method for the coupled mode equations,the effects of three coupling coefficientsκcoL,κclL,andκsL on the transmission and re-flection spectra of SFG have been investigated.The simulations show that the overall intensity of the transmission spectrum of SFG is decided by LPFG,that the main lobes of the transmission and reflectivity spectra of SFG are decided by coupling coefficientsκcoL andκsL,and that the side lobes of the transmission and reflectivity spectra are decided by coupling coefficientsκclL andκsL.展开更多
The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and bounda...The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.展开更多
In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface...In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface mechanics cannot be ignored.This paper focuses on studying the impact of micro-structural effect on interface crack propagation.Modified couple stress theory(MCST)is used to study the buckling delamination of ultra-thin film-substrate systems.The equivalent elastic modulus(EEM)and equivalent flexural rigidity(EFR)are derived based on MCST.Substituting EEM and EFR into the classical Kirchhoff plate theory,the governing equations of ultra-thin film-substrate system with micro-structural effect can be obtained.The finite element method(FEM)was used to calculate the critical strain energy release rate for crack extension.Differences between the three theoretical approaches of MCST,classical theory(CT),and FEM were compared.The effects of stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters on crack extension were analyzed.The results show that the FEM calculations coincide with the CT calculations.The stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters have significantly influence crack extension.展开更多
基金Major Program of National Natural Science Foundation of China,No.41942004,No.41590842。
文摘A near-distance,nonlinear coupling relationship objectively exists between urbanization and the eco-environment.The issue of how to coordinate the relationship between them has become a global strategic and scientific issue.This study reveals the nature,relationship and intensity of coupling between urbanization and the eco-environment from a theoretical perspective.Based on the strength of coupling,relationships can be characterized as having very-low,low,medium,high,very-high or full coupling intensity,which correspond to the categories of random coupling,indirect coupling,loose coupling,cooperative coupling,close coupling,and controlled coupling.Together,these make up an urbanization and eco-environment"coupling tower."This study also develops an urbanization and eco-environment coupling circle theory and generates 45 coupling graphs(including linear,exponential-curve,logarithmic-curve,double exponential-curve and S-curve graphs)per 10°of rotation of the coupling circle,with different graphs corresponding to different urban development stages and development models.Of the various coupling graphs,the S-curve graph is considered the optimum,as it reflects the best interactivity scenario between urbanization and the eco-environment.Using an S-curve coupling graph,and with the help of an SD model and based on the complex one-to-one,one-to-many,and many-to-many relationships between the variables,this study develops the Urbanization and Eco-environment Coupler(UEC).The UEC is composed of 11 regulating elements and 201 variables.If one variable changes,it changes the whole,affecting the structure,function and regulation of the entire coupler.The UEC includes three spatio-temporal scales:static regulation between multiple urbanization areas and eco-environment areas at the same time,dynamic regulation between the same urbanization area and eco-environment area at different times,and dynamic regulation between multiple urbanization areas and eco-environment areas at different times.Regulation gradually promotes evolution from low-level coupling to high-level coupling between urbanization and the eco-environment.
文摘<div style="text-align:justify;"> Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail. </div>
基金the National Natural Science Foundation of China(No.19832040)
文摘Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.
基金Supported by the Start-Up Funds of Xi’an Polytechnic University under Grant No BS1211the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 2013JK0679
文摘Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp （n=Q, 5）, combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin-orbit coupling. Spin-orbit coupling is included in the post Hartree-Fock procedure, i.e., in the coupled- cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.
基金supported by the National Natural Science Foundation of China(Grant No.G0501040161101040)
文摘Planar Bragg reflector operating in the sub-terahertz wavelength installed at the upstream end of a sheet beam back- ward wave oscillator （BWO） is very promising to minimize the whole circuit structure and make it more compact. In this paper, a sub-terahertz wavelength （0.18-0.22 THz） tunable planar Bragg reflector is numerically analyzed by using multi-mode coupling theory （MCT）. The operating mode TE10 and dominant coupling mode TE01 are mainly considered in this theory. Reflection and transmission performance of the reflector are demonstrated in detail and the results, in excellent agreement with the theoretical analysis and simulation, are also presented in this paper. Self- and cross-coupling coefficients between these two modes are presented as well. The reflector behaviors with different Bragg dimensions are discussed and analyzed in the 0.16-0.22 THz range. The analysis in this paper can be of benefit to the design and fabrication of the whole BWO circuit.
文摘A non-classical Kirchhoff plate model is developed for the dynamic analysis of microscale plates based on the modified couple stress theory in which an internal material length scale parameter is included. Unlike the classical Kirchhoff plate model, the newly developed model can capture the size effect of microscale plates. Two boundary value problems of rectangular micro- plates are solved and the size effect on the lowest two natural frequencies is investigated. It is shown that the natural frequencies of the microscale plates predicted by the current model are size-dependent when the plate thickness is comparable to the material length scale parameter.
文摘Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.
基金The authors would like to thank the Iranian Nanotechnology Development Committee for their financial support.
文摘Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.
文摘The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.
文摘The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.
基金supported by the National Natural Sciences Foundation of China(No.11572204)
文摘In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh–Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon reveals that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli–Euler beam and material isotropy.
文摘A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.
基金Project supported by the Funds of the Natural Science Foundation of Guangdong Province(Nos.S2013010012463 and S2013010014485)the Excellent Teacher Scheme in Guangdong Higher Education Institutions(No.Yq2014332)the Funds of the Guangdong college discipline construction(Nos.2013KJCX0189 and 2014KZDXM063)
文摘In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.
文摘The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.
基金supported by the National Natural Science Foundation of China (11172138, 10727201)
文摘This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.
基金supported by the National Natural Science Foundation of China(Nos.51505089 and61204116)the Opening Project of the Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory(Nos.ZHD201207 and 9140C030605140C03015)the Pearl River S&T Nova Program of Guangzhou(No.2014J2200086)
文摘An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.
基金Project supported by the National Natural Science Foundation of China(Nos.11672336,12072374)。
文摘A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.
基金Supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(708064)Natural Science Foundation of Wuhan University of Technology(471-38650024)
文摘For the superstructure fiber grating(SFG)consisting of fiber Bragg grating(FBG)and long-period fiber grating(LPFG),there exist three kinds of coupling:the contra-directional coupling between forward propagating core mode and backward propagating core mode,the contra-directional coupling between core mode and cladding mode,and the co-directional coupling between core mode and cladding mode.By using the similarity transformation method for the coupled mode equations,the effects of three coupling coefficientsκcoL,κclL,andκsL on the transmission and re-flection spectra of SFG have been investigated.The simulations show that the overall intensity of the transmission spectrum of SFG is decided by LPFG,that the main lobes of the transmission and reflectivity spectra of SFG are decided by coupling coefficientsκcoL andκsL,and that the side lobes of the transmission and reflectivity spectra are decided by coupling coefficientsκclL andκsL.
基金supported in part by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
基金supported by the National Key R&D Program of China(No.2022YFB3207100)the Hubei Provincial Strategic Scientist Training Plan(No.2022EJD009)the Fundamental Research Funds for the Central Universities(No.2042023kf1041).
文摘In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface mechanics cannot be ignored.This paper focuses on studying the impact of micro-structural effect on interface crack propagation.Modified couple stress theory(MCST)is used to study the buckling delamination of ultra-thin film-substrate systems.The equivalent elastic modulus(EEM)and equivalent flexural rigidity(EFR)are derived based on MCST.Substituting EEM and EFR into the classical Kirchhoff plate theory,the governing equations of ultra-thin film-substrate system with micro-structural effect can be obtained.The finite element method(FEM)was used to calculate the critical strain energy release rate for crack extension.Differences between the three theoretical approaches of MCST,classical theory(CT),and FEM were compared.The effects of stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters on crack extension were analyzed.The results show that the FEM calculations coincide with the CT calculations.The stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters have significantly influence crack extension.
