In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed o...In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.展开更多
This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulate...This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate(SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of Ba Ti O3/Co Fe2 O4. The refined zigzag theory(RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton’s principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.展开更多
Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing ...Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing equations for nonlinear vibrations are obtained though the balance of forces.The Galerkin method is employed to obtain the approximate solutions for nonlinear free and forced vibrations of the FGM laminates.Numerical results show that considering surface effects changes the equivalent Young’s modulus and bending stiffness of FGM sandwich nanoplates.In addition,the influences of surface effects are related to the geometric size of the nanoplate.Numerical examples are proposed to verify the effectiveness of the present results.展开更多
This research develops an analytical approach to explore the wave propagation problem of piezoelectric sandwich nanoplates.The core of the sandwich nanoplates is a nanocomposite layer reinforced with graphene platelet...This research develops an analytical approach to explore the wave propagation problem of piezoelectric sandwich nanoplates.The core of the sandwich nanoplates is a nanocomposite layer reinforced with graphene platelets,which is integrated by two piezoelectric layers exposed to electric field.The material properties of nanocomposite layer are obtained by the Halpin–Tsai model and the rule of mixtures.The Euler–Lagrange equations of nanoplates are derived from Hamilton’s principle.By using the nonlocal strain gradient theory,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of propagation angle,small-scale and external loads on wave frequency.The results reveal that the frequency changes periodically with the propagation angle and can be reduced by increasing voltage,temperature and the thickness of graphene platelets.展开更多
Αn analytical method is developed to explore the wave propagation characteristics of piezoelectric sandwich nanoplates in the present work.The sandwich nanoplates are composed of a graphene reinforced composite core ...Αn analytical method is developed to explore the wave propagation characteristics of piezoelectric sandwich nanoplates in the present work.The sandwich nanoplates are composed of a graphene reinforced composite core layer with two piezoelectric surface layers exposed to electric field.The material properties of the nanocomposite layer are given by the Halpin–Tsai model and mixture’s rule.The Euler–Lagrange equation of the nanoplates is obtained by Hamilton's principle and first-order shear deformation theory.Then,combining the high-order nonlocal strain gradient theory with the hygrothermal constitutive relationship of composite nanoplates,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of scale parameters,applied external voltage,temperature variation,moisture variation,graphene size,and weight fraction on wave frequency.The results reveal that low-order and high-order nonlocal parameters and length scale parameters have different effects on wave frequency.The wave frequency can be reduced by increasing temperature and the thickness of graphene.This could facilitate the investigation of the dynamic properties of graphene nanocomposite structures.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11502218,11672252,11602204,and 12102373)the Fundamental Research Funds for the Central Universities of China(No.2682020ZT106)。
文摘In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.
基金Project supported by the University of Kashan(No.574600/33)
文摘This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic(MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate(SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of Ba Ti O3/Co Fe2 O4. The refined zigzag theory(RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton’s principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.
基金supported by the Natural Science Foundation of Hebei Province(A2022203025)the Science and Technology Project of Hebei Education Department(ZD2021104).
文摘Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing equations for nonlinear vibrations are obtained though the balance of forces.The Galerkin method is employed to obtain the approximate solutions for nonlinear free and forced vibrations of the FGM laminates.Numerical results show that considering surface effects changes the equivalent Young’s modulus and bending stiffness of FGM sandwich nanoplates.In addition,the influences of surface effects are related to the geometric size of the nanoplate.Numerical examples are proposed to verify the effectiveness of the present results.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11502218,11672252 and 11602204)the Fundamental Research Funds for the Central Universities of China(Grant No.2682020ZT106).
文摘This research develops an analytical approach to explore the wave propagation problem of piezoelectric sandwich nanoplates.The core of the sandwich nanoplates is a nanocomposite layer reinforced with graphene platelets,which is integrated by two piezoelectric layers exposed to electric field.The material properties of nanocomposite layer are obtained by the Halpin–Tsai model and the rule of mixtures.The Euler–Lagrange equations of nanoplates are derived from Hamilton’s principle.By using the nonlocal strain gradient theory,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of propagation angle,small-scale and external loads on wave frequency.The results reveal that the frequency changes periodically with the propagation angle and can be reduced by increasing voltage,temperature and the thickness of graphene platelets.
基金This work was supported in part by the National Natural Science Foundation of China(Grants 11502218,11672252,and 11602204)the Fundamental Research Funds for the Central Universities of China(Grant 2682020ZT106).
文摘Αn analytical method is developed to explore the wave propagation characteristics of piezoelectric sandwich nanoplates in the present work.The sandwich nanoplates are composed of a graphene reinforced composite core layer with two piezoelectric surface layers exposed to electric field.The material properties of the nanocomposite layer are given by the Halpin–Tsai model and mixture’s rule.The Euler–Lagrange equation of the nanoplates is obtained by Hamilton's principle and first-order shear deformation theory.Then,combining the high-order nonlocal strain gradient theory with the hygrothermal constitutive relationship of composite nanoplates,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of scale parameters,applied external voltage,temperature variation,moisture variation,graphene size,and weight fraction on wave frequency.The results reveal that low-order and high-order nonlocal parameters and length scale parameters have different effects on wave frequency.The wave frequency can be reduced by increasing temperature and the thickness of graphene.This could facilitate the investigation of the dynamic properties of graphene nanocomposite structures.
