A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress the...A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).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
The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are p...The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.展开更多
The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elas...The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with 展开更多
In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple st...In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple stress theory （MCST） is con- sidered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton＇s principle. The differential quadrature method （DQM） in conjunction with the Bolotin method is used in order to calculate the dynamic instability region （DIR） of SWCNTs. The effects of differ- ent parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The re- sults depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system （NEMS） and micro-electro-mechanical system （MEMS）.展开更多
基金the National Natural Science Foundation of China(Nos.11602204 and 12102373)the Fundamental Research Funds for the Central Universities of China(Nos.2682022ZTPY081 and 2682022CX056)the Natural Science Foundation of Sichuan Province of China(Nos.2023NSFSC0849,2023NSFSC1300,2022NSFSC1938,and 2022NSFSC2003)。
文摘A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).
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Project supported by the National Key Research and Development Program of China(No.2017YFC0307604)the Talent Foundation of China University of Petroleum(No.Y1215042)the Graduate Innovation Program of China University of Petroleum(East China)(No.YCX2019084)
文摘The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.
基金supported by the Iranian Nanotechnology Development Committee and the University of Kashan(No.363452/10)
文摘The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with
文摘In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple stress theory （MCST） is con- sidered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton＇s principle. The differential quadrature method （DQM） in conjunction with the Bolotin method is used in order to calculate the dynamic instability region （DIR） of SWCNTs. The effects of differ- ent parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The re- sults depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system （NEMS） and micro-electro-mechanical system （MEMS）.
