The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler...The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.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
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 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
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
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
This paper presents an analytical solution for the interaction of electric potentials,electric displacement,elastic deformations,and describes hygrothermal effect responses in hollow and solid cylinders,subjected to m...This paper presents an analytical solution for the interaction of electric potentials,electric displacement,elastic deformations,and describes hygrothermal effect responses in hollow and solid cylinders,subjected to mechanical load and electric potential.Exact solutions for displacement,stresses and electric potentials in functionally graded piezoelectric material are determined using the infinitesimal theory.The material properties coefficients of the present cylinder are assumed to be graded in the radial direction by a power law distribution.Numerical examples display the significant of influence of material inhomogeneity.It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the piezoelectric hollow and solid cylinders responses,which will be of particular importance in modern engineering designs.展开更多
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through a large research project(No.RGP2/80/45)。
文摘The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.
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.
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 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.
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This paper presents an analytical solution for the interaction of electric potentials,electric displacement,elastic deformations,and describes hygrothermal effect responses in hollow and solid cylinders,subjected to mechanical load and electric potential.Exact solutions for displacement,stresses and electric potentials in functionally graded piezoelectric material are determined using the infinitesimal theory.The material properties coefficients of the present cylinder are assumed to be graded in the radial direction by a power law distribution.Numerical examples display the significant of influence of material inhomogeneity.It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the piezoelectric hollow and solid cylinders responses,which will be of particular importance in modern engineering designs.
