Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power l...Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.展开更多
In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and ...In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.展开更多
This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is deriv...This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.展开更多
In this paper, we proposed a general form of a multi-team Bertrand game. Then, we studied a two-team Bertrand game, each team consists of two firms, with heterogeneous strategies among teams and homogeneous strategies...In this paper, we proposed a general form of a multi-team Bertrand game. Then, we studied a two-team Bertrand game, each team consists of two firms, with heterogeneous strategies among teams and homogeneous strategies among players. We find the equilibrium solutions and the conditions of their local stability. Numerical simulations were used to illustrate the complex behaviour of the proposed model, such as period doubling bifurcation and chaos. Finally, we used the feedback control method to control the model.展开更多
In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have ...In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is available for the first disk while the exact analytical solution is not available for the second annular disk. Both exact and numerical results for stress function, stresses, strains and radial displacement will be investigated for the first annular disk of variable thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second rotating variable-thickness annular disk is investigated. Finally, the distributions of stress function, displacement, strains, and stresses will be presented. The appropriate comparisons and discussions are made at the same angular velocity.展开更多
In this paper, an analytical solution for the rotation problem of an inhomogeneous hollow cylinder with variable thickness under plane strain assumption is developed. The present cylinder is made of a fiber-reinforced...In this paper, an analytical solution for the rotation problem of an inhomogeneous hollow cylinder with variable thickness under plane strain assumption is developed. The present cylinder is made of a fiber-reinforced viscoelastic inhomogeneous orthotropic material. The thickness of the cylinder is taken as parabolic function in the radial direction. The elastic properties varies in the same manner as the thickness of the cylinder while the density varies according to an exponential law form. The inner and outer surfaces of the cylinder are considered to have combinations of free and clamped boundary conditions. Analytical solutions are given according to different types of the hollow cylinders. An extension of the present solutions to the viscoelastic ones and some applications are investigated in Part II.展开更多
Analytical solutions for the rotating variable-thickness inhomogeneous, orthotropic, hollow cylinders under plane strain assumption are developed in Part I of this paper. The extensions of these solutions to the visco...Analytical solutions for the rotating variable-thickness inhomogeneous, orthotropic, hollow cylinders under plane strain assumption are developed in Part I of this paper. The extensions of these solutions to the viscoelastic case are discussed here. The method of effective moduli and Illyushin's approximation method are used for this purpose. The rotating fiber-reinforced viscoelastic homogeneous isotropic hollow cylinders with uniform thickness are obtained as special cases of the studied problem. Numerical application examples are given for the dimensionless displacement of and stresses in the different cylinders. The influences of time, constitutive parameter and elastic properties on the stresses and displacement are investigated.展开更多
The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with inter...The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem;using different theories of generalized thermoelasticity;has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.展开更多
Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagati...Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.展开更多
Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and ...Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.展开更多
This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a M...This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.展开更多
The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isotherma...The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.展开更多
In this paper,free vibration,wave propagation,and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the ...In this paper,free vibration,wave propagation,and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler–Bernoulli beam theory.The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials.A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam.Hamilton principal is used to derive governing differential equations of motion.Three behaviors of sandwich microbeam including free vibration,wave propagation,and bending analyses are studied in this paper.Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index,applied voltage,parameters of foundation,and material length scales.The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied.展开更多
The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velo...The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.展开更多
An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a hetero...An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material. It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions, the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin＇s approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness variation, constitutive, time parameters on the radial displacement, and stresses are investigated.展开更多
The mixed first-order shear deformation plate theory（MFPT） is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasterna...The mixed first-order shear deformation plate theory（MFPT） is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasternak＇s model or Winkler＇s model of elastic foundation or without any elastic foundation.Several examples are presented to verify the accuracy of the present theory.Numerical results for deflection and stresses are presented.The proposed MFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic foundation.The results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio.展开更多
Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak＇s foundation is studied in this paper. Timoshenko＇s beam model and nonlocal elasticity theory ar...Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak＇s foundation is studied in this paper. Timoshenko＇s beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton＇s principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.展开更多
The bending response for exponentially graded composite （EGC） sandwich plates is investigated. The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate t...The bending response for exponentially graded composite （EGC） sandwich plates is investigated. The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories. Four types of sand- wich plates are considered taking into account the symmetry of the plate and the thickness of each layer. The effective moduli and Illyushin＇s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates. Then numerical results for deflections and stresses are presented and the effects due to time parameter, aspect ratio, side-to-thickness ratio and constitutive parameter are investigated.展开更多
In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundatio...In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.展开更多
文摘Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.
文摘In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.
文摘This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.
文摘In this paper, we proposed a general form of a multi-team Bertrand game. Then, we studied a two-team Bertrand game, each team consists of two firms, with heterogeneous strategies among teams and homogeneous strategies among players. We find the equilibrium solutions and the conditions of their local stability. Numerical simulations were used to illustrate the complex behaviour of the proposed model, such as period doubling bifurcation and chaos. Finally, we used the feedback control method to control the model.
文摘In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is available for the first disk while the exact analytical solution is not available for the second annular disk. Both exact and numerical results for stress function, stresses, strains and radial displacement will be investigated for the first annular disk of variable thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second rotating variable-thickness annular disk is investigated. Finally, the distributions of stress function, displacement, strains, and stresses will be presented. The appropriate comparisons and discussions are made at the same angular velocity.
文摘In this paper, an analytical solution for the rotation problem of an inhomogeneous hollow cylinder with variable thickness under plane strain assumption is developed. The present cylinder is made of a fiber-reinforced viscoelastic inhomogeneous orthotropic material. The thickness of the cylinder is taken as parabolic function in the radial direction. The elastic properties varies in the same manner as the thickness of the cylinder while the density varies according to an exponential law form. The inner and outer surfaces of the cylinder are considered to have combinations of free and clamped boundary conditions. Analytical solutions are given according to different types of the hollow cylinders. An extension of the present solutions to the viscoelastic ones and some applications are investigated in Part II.
文摘Analytical solutions for the rotating variable-thickness inhomogeneous, orthotropic, hollow cylinders under plane strain assumption are developed in Part I of this paper. The extensions of these solutions to the viscoelastic case are discussed here. The method of effective moduli and Illyushin's approximation method are used for this purpose. The rotating fiber-reinforced viscoelastic homogeneous isotropic hollow cylinders with uniform thickness are obtained as special cases of the studied problem. Numerical application examples are given for the dimensionless displacement of and stresses in the different cylinders. The influences of time, constitutive parameter and elastic properties on the stresses and displacement are investigated.
文摘The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem;using different theories of generalized thermoelasticity;has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.
文摘Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.
文摘Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.
文摘This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under grant No.(363/130/1431)
文摘The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.
基金The research described in this paper was financially supported by the University of Kashan[grant number:574613/027].The first author would like to thank the Iranian Nanotechnology Development Committee for their financial support.
文摘In this paper,free vibration,wave propagation,and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler–Bernoulli beam theory.The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials.A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam.Hamilton principal is used to derive governing differential equations of motion.Three behaviors of sandwich microbeam including free vibration,wave propagation,and bending analyses are studied in this paper.Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index,applied voltage,parameters of foundation,and material length scales.The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied.
文摘The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.
文摘An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material. It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions, the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin＇s approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness variation, constitutive, time parameters on the radial displacement, and stresses are investigated.
文摘The mixed first-order shear deformation plate theory（MFPT） is employed to study the bending response of simply-supported orthotropic plates.The present plate is subjected to a mechanical load and resting on Pasternak＇s model or Winkler＇s model of elastic foundation or without any elastic foundation.Several examples are presented to verify the accuracy of the present theory.Numerical results for deflection and stresses are presented.The proposed MFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic foundation.The results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio.
基金financially supported by the University of Kashan(Grant Number:363460/5)Iranian Nanotechnology Development Committee(Grant Number:1396/17)
文摘Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak＇s foundation is studied in this paper. Timoshenko＇s beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton＇s principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.
文摘The bending response for exponentially graded composite （EGC） sandwich plates is investigated. The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories. Four types of sand- wich plates are considered taking into account the symmetry of the plate and the thickness of each layer. The effective moduli and Illyushin＇s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates. Then numerical results for deflections and stresses are presented and the effects due to time parameter, aspect ratio, side-to-thickness ratio and constitutive parameter are investigated.
文摘In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.
