Nonlocal thermal vibrations of embedded nanoplates in a viscoelastic medium

Ashraf M. Zenkour 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.82 No.6

The nonlocal elasticity as well as Mindlin’s first-order shear deformation plate theory are proposed to investigate thermal vibrational of a nanoplate placing on a three-factor foundation. The Winkler-Pasternak elastic foundation is connected with the viscous damping to obtain the present three-parameter viscoelastic model. Differential equations of motion are derived and resolved for simply-supported nanoplates to get their natural frequencies. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. A comparison example is dictated to validate the precision of present results. Effects of other factors such as aspect ratio, mode numbers, and foundation parameters are discussed carefully for the vibration problem. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for comparisons with future investigations.

Thermoelastic solutions for annular disks with arbitrary variable thickness

Zenkour, Ashraf M. Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.24 No.5

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.

The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating

Zenkour, Ashraf M.,Abouelregal, Ahmed E. Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.2

The present investigation is concerned with the effect of two temperatures on functionally graded (FG) nanobeams subjected to sinusoidal pulse heating sources. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is fully ceramic whereas the lower surface is fully metal. The generalized two-temperature nonlocal theory of thermoelasticity in the context of Lord and Shulman's (LS) model is used to solve this problem. The governing equations are solved in the Laplace transformation domain. The inversion of the Laplace transformation is computed numerically using a method based on Fourier series expansion technique. Some comparisons have been shown to estimate the effects of the nonlocal parameter, the temperature discrepancy and the pulse width of the sinusoidal pulse. Additional results across the thickness of the nanobeam are presented graphically.

A comparative study for bending of cross-ply laminated plates resting on elastic foundations

Ashraf M. Zenkour 국제구조공학회 2015 Smart Structures and Systems, An International Jou Vol.15 No.6

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

Vibration analysis of generalized thermoelastic microbeams resting on visco-Pasternak's foundations

Zenkour, Ashraf M. Techno-Press 2017 Advances in aircraft and spacecraft science Vol.4 No.3

The natural vibration analysis of microbeams resting on visco-Pasternak's foundation is presented. The thermoelasticity theory of Green and Naghdi without energy dissipation as well as the classical Euler-Bernoulli's beam theory is used for description of natural frequencies of the microbeam. The generalized thermoelasticity model is used to obtain the free vibration frequencies due to the coupling equations of a simply-supported microbeam resting on the three-parameter viscoelastic foundation. The fundamental frequencies are evaluated in terms of length-to-thickness ratio, width-to-thickness ratio and three foundation parameters. Sample natural frequencies are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

Bending response of functionally graded piezoelectric plates using a two-variable shear deformation theory

Zenkour, Ashraf M.,Hafed, Zahra S. Techno-Press 2020 Advances in aircraft and spacecraft science Vol.7 No.2

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux

Ashraf M. Zenkour,Ahmed E. Abouelregal 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.4

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

EFFECTS OF PHASE-LAGS AND VARIABLE THERMAL CONDUCTIVITY IN A THERMOVISCOELASTIC SOLID WITH A CYLINDRICAL CAVITY

Zenkour, Ashraf M. The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.3

This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman's model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman's model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.

Buckling of a single-layered graphene sheet embedded in visco-Pasternak's medium via nonlocal first-order theory

Zenkour, Ashraf M. Techno-Press 2016 Advances in nano research Vol.4 No.4

The buckling response of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak's medium is presented. The nonlocal first-order shear deformation elasticity theory is used for this purpose. The visco-Pasternak's medium is considered by adding the damping effect to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus. The SLGS be subjected to distributive compressive in-plane edge forces per unit length. The governing equilibrium equations are obtained and solved for getting the critical buckling loads of simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak's foundation, damping coefficient, and mode numbers on the buckling analysis of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

EFFECTS OF PHASE-LAGS AND VARIABLE THERMAL CONDUCTIVITY IN A THERMOVISCOELASTIC SOLID WITH A CYLINDRICAL CAVITY

( Ashraf M. Zenkour ) 호남수학회 2016 호남수학학술지 Vol.38 No.3

This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman`s model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman`s model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.