Nonlocal Thermoelasticity Research Articles

Rotating magneto-thermoelastic rod with finite length due to moving heat sources via Eringen’s nonlocal model

The article is concerned with a new nonlocal model based on Eringen’s nonlocal elasticity and generalized thermoelasticity. A study is made of the magneto-thermoelastic waves in an isotropic conducting thermoelastic finite rod subjected to moving heat sources permeated by a primary uniform magnetic field and rotating with a uniform angular velocity. The Laplace transform technique with respect to time is utilized. The inverse transforms to the physical domain are obtained in a numerical manner for the nonlocal thermal stress, temperature, and displacement distributions. Finally, some graphical presentations have been made to assess the effects of various parameters; nonlocal parameter, rotating, applied magnetic field as well as the speed of the heat source on the field variables. The results obtained in this work should be useful for researchers in nonlocal material science, low-temperature physicists, new materials designers, as well as to those who are working on the development of the theory of nonlocal thermoelasticity.

Thermoelastic Vibration of Temperature-Dependent Nanobeams Due to Rectified Sine Wave Heating—A State Space Approach

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The effects of nonlocal parameter and angular frequency on the thermal vibration quantities are discussed. The results of all quantities are illustrated graphically and investigated.

Effect of nonlocal thermoelasticity on buckling of axially functionally graded nanobeams

In this work, the thermal effect on the buckling response of the axially functionally graded (AFG) nanobeams is studied based on the nonlocal thermoelasticity theory. Size effects of elastic deformation and heat conduction are considered simultaneously. Non-uniform distribution of temperature along the longitudinal direction of the AFG nanobeams is taken into account and determined by the nonlocal heat conductive law. Equations of motion and the corresponding boundary conditions are derived with the aid of the variational principle within the sinusoidal shear deformation theory and the nonlocal thermoelasticity theory. Ritz method is used to obtain the solutions for the thermal buckling response of the AFG nanobeams with various boundary conditions. Numerical results addressing the significance of the AFG index, the nonlocal parameters of elasticity and heat conduction, and the transverse shear deformation on the buckling behavior are displayed. It is found that, in addition to the nonlocal effect of elasticity, the nonlocal heat conduction plays an important role in analyzing the thermal–mechanical behaviors of the FG nanostructures.

Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory

In this paper, the analytical approach for thermal stress and deformation analysis of a curved nanobeam is presented. The nanobeam is subjected to transverse mechanical and thermal loads while resting on Pasternak's foundation. Sinusoidal shear deformation theory is employed to derive displacement field of curved nanobeam. In addition, nonlocal thermo-elasticity relations are employed to derive governing equations of thermal analysis based on principle of virtual work. The analytical results are presented for simply-supported curved nanobeam to discuss the influence of important parameters on the results of thermal stress. The important parameters include spring and shear parameters of foundation, thermal loads, nonlocal parameter and radius of curvature of curved nanobeam. The results of our problem are applicable to design of curved nanobeams subjected to thermal and mechanical loads.

Dynamic response of a nanobeam induced by ramp-type heating and subjected to a moving load

The problem considered is that of an isotropic, thermoelastic nanobeam subjected to a moving concentrated loading. The solution of the problem is presented in the context of generalized theory of nonlocal thermoelasticity. Modal analysis along with Laplace’s transform technique is employed to obtain analytical solution of the governing partial differential equations. Effect of velocity of the moving load, nonlocal parameter and ramping-time parameter on dynamic deflection, temperature and flexural moment of the nanobeam has been investigated. Numerical results obtained from the present study are presented graphically and discussed.

Size-dependent damping of a nanobeam using nonlocal thermoelasticity: extension of Zener, Lifshitz, and Roukes’ damping model

Thermoelastic damping is an important issue for micro-/nanoscale mechanical resonators. In this work, an Euler–Bernoulli beam with different types of mechanical boundary conditions at the two ends is adopted. Once it bends, the half compressed (stretched) will be heated (cooled), then a transverse heat conduction appears, and energy dissipation occurs. First, size-dependent thermoelasticity based on generalized thermodynamics is introduced by combining the nonlocal elasticity and hydrodynamic heat-conductive model heat conduction, and the governing equations of the nonlocal thermal Euler–Bernoulli beam are sequently formulated. Second, an analytical solution to the inverse quality factor is obtained by using the complex-frequency approach, and it is observed that the solution is related to the nonlocal parameter of both elastic and thermal fields, as well as material constants. Meanwhile, another numerical method to get the inverse quality factor is proposed. Third, the effects of nonlocal parameters of both thermal and elastic fields, the height of the beam, and the material constants on the quality factor are evaluated. Finally, conclusive remarks are summarized. The predicted results are expected to be beneficial to micro-/nanomechanical resonators design.

Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity

Abstract Thermoelastic analysis at micro and nano-scale is becoming important along with the miniaturization of the device and wide application of ultrafast lasers, even the novel laser burst technology, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. In this work, a size-dependent thermoelastic model is established for higher order simple material by adopting both the size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free energy. It is proven that the present model is in essence identical to the coupling of nonlocal heat conductive law (GK model) and nonlocal elastic (stress gradient) model. Also, higher order boundary conditions for stress tensor and heat flux are presented and discussed. For numerical evaluation, a bi-layered structure is considered with interfacial thermal contact resistance and elastic wave impendence incorporated. From numerical results, the effects of size-dependent characteristic lengths and material constants of each layer on the transient responses are discussed, systematically. This study is expected to be helpful for theoretical modeling of thermoelasticity at nano-scale, and may be beneficial to design of nano-sized and multi-layered devices.

BENDING VIBRATION AND STABILITY OF A MULTIPLE-NANOBEAM SYSTEM INFLUENCED BY TEMPERATURE CHANGE

In this study, we analyzed the bending vibration and stability of a multiple-nanobeam system (MNBS) coupled in elastic medium and influenced by temperature change and compressive axial load. The MNBS is modeled as the system consisting of a set of m identical and simply supported nanobeams mutually connected by Winkler’s type elastic layers. According to the Euler - Bernoulli beam and nonlocal thermo-elasticity theory, the system of m coupled partial differential equations is derived and solved by means of the method of separation of variables as well as the trigonometric one. Analytical solutions for natural frequencies and critical buckling loads of elastic MNBS are obtained. The effects of nonlocal parameter, temperature change and the number of nanobeams on the natural frequencies and the buckling loads are investigated through numerical examples. Thus, this work can represent a starting point to examine dynamical behavior and design of complex nanobeam structures, nanocomposites and nanodevices under the influence of various physical fields.

Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity

Buckling analysis of nanobeam is significantly important for design of nano-electro-mechanical systems (NEMS), especially for those under non-uniform temperature induced commonly by the operation of NEMS. In this work, such issue is investigated with the aids of size-dependent model, i.e. nonlocal thermoelasticity, and size effect of heat conduction on buckling property is considered for the first time. Euler–Bernoulli beam is adopted and reformulated within nonlocal theory. Analytical solution to critical load for various boundary conditions, e.g. SS, CF, CS and CC, is obtained using eigenvalue method. And the temperature distribution is determined using nonlocal heat conductive law. The effect of elastic and thermal nonlocal parameter on the critical load is systematically discussed. It is observed that classical models over-predict the critical load, which may be dangerous in practical applications. The present work is expected to be helpful for design of nanobeam-based devices and systems.

Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions

A model of nonlocal thermoelasticity theory of Green and Naghdi without energy dissipation is used to consider the vibration behavior of a nano-machined resonator. The nonlocality brings in an internal length scale in the formulation and, thus, allows for the interpretation of size effects. The governing frequency equation is given for nanobeams subjected to different boundary conditions. A combination of simply-supported, clamped, and free boundary conditions is investigated. The effect of side-to-thickness and aspect ratios, as well as the influence of either nonlocal parameter or thermoelastic coupling are all investigated. In addition, the effect of environmental temperature T0 on the vibration frequency is also investigated.

State space approach for the vibration of nanobeams based on the nonlocal thermoelasticity theory without energy dissipation

In this article, an Euler-Bernoulli beam model based upon nonlocal thermoelasticity theory without energy dissipation is used to study the vibration of a nanobeam subjected to ramp-type heating. Classical continuum theory is inherently size independent, while nonlocal elasticity exhibits size dependence. Among other things, this leads to a new expression for the effective nonlocal bending moment as contrasted to its classical counterpart. The thermal problem is addressed in the context of the Green-Naghdi (GN) theory of heat transport without energy dissipation. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of modern control theory. Inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of nonlocality and ramping time parameters on the lateral vibration, temperature, displacement and bending moment are discussed.

Nonlinear effects of thermo-sensitive nanobeams via a nonlocal thermoelasticity model with relaxation time

This paper presents a theoretical nonlocal model for a thermo-sensitive nanobeam based on the generalized thermoelasticity theory with thermal relaxation time. The present nanobeam is subjected to a sinusoidal pulse varying heat and its thermal conductivity is considered to be variable. This article deals with a nonlinear coupling partial differential equation since the thermal conductivity depends on temperature. The nonlocal theories of coupled thermoelasticity can be extracted as limited and special case of the present model. The effect of the variability thermal conductivity parameter, the nonlocal parameter, the relaxation time and the pulse width of the sinusoidal pulse on the distribution of lateral vibration, the temperature and the displacement of the nanobeam is investigated.

The Nonlocal Dual Phase Lag Model of a Thermoelastic Nanobeam Subjected to a Sinusoidal Pulse Heating

This paper investigates the vibration phenomenon of a nanobeam subjected to a sinusoidal pulse varying heat. A unified generalized nonlocal thermoelasticity model with dual phase lag (DPL) is deduced to solve this problem. The nonlocal theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can be extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and the temperature. The inverse of Laplace transforms is computed numerically using Fourier expansion techniques. The effects of the nonlocal parameter, the phase lags, and the pulse width of the sinusoidal pulse are studied on the lateral vibration, the temperature, and the displacement of the nanobeam. Comparisons among the effects of the phase lags and the pulse width are discussed.

A refined nonlocal thermoelasticity theory for the vibration of nanobeams induced by ramp-type heating

For small volumes at the micrometer and nanometer level, classical continuum mechanics cannot be used to capture experimentally observed phenomena, such as size effects. Moreover, dissipation is much less pronounced than that in the case of macroscopic volume elements. To remedy the situation, generalized continuum mechanics theories should be used as an alternative to molecular dynamics simulations which do provide physical insight, but may not be suitable for engineering applications and the formulation of related boundary value problems. The present contribution is an example in this direction. An Euler–Bernoulli beam model is constructed to study the vibration of a nanobeam subjected to ramp-type heating. A generalized thermoelasticity theory with non-local deformation effects and dual-phase-lag (DPL) or time-delay thermal effects is used to address this problem. An analytical technique based on Laplace transform is employed. The inverse of Laplace transform is computed numerically using Fourier expansion techniques. The effects of nonlocality, DPLs, and the ramping-time parameter on the lateral vibration, the temperature, the displacement and the flexural moment of the nanobeam are discussed. The results are shown quantitatively in corresponding graphs.

Weakly nonlocal thermoelasticity for microstructured solids: microdeformation and microtemperature

Prediction of the thermoelastic behavior of microstructured materials suggests a more general description of thermal processes in addition to the generalized continuum description extending the conventional continuum mechanics for incorporating intrinsic microstructural effects. Double dual internal variables are introduced in order to couple inertial microstructural effects like microdeformation and diffusive microstructural effects like microtemperature. The full coupled system of governing equations provides a complete extension of the classical thermoelasticity theory onto the case of microstructured solids.

Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model

The vibration of functionally graded (FG) nanobeams subjected to a sinusoidal pulse-heating source is investigated. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is pure ceramic, whereas the lower surface is pure metal. The generalized nonlocal thermoelasticity model based on Lord and Shulman’s theory is used to solve this problem. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and temperature. The inverse Laplace transforms are computed numerically using Fourier expansion techniques. A comparison between the obtained results from the nonlocal theory and those from the local theory of coupled thermoelasticity is presented. The effect of the nonlocal parameter, the pulse width of the sinusoidal pulse, is studied on the lateral vibration, the temperature and the displacement of the nanobeam. Additional results across the thickness of the nanobeam are presented graphically.

Some theorems in generalized nonlocal thermoelasticity

A reciprocity theorem in the context of the generalized thermoelasticity is established. A uniqueness theorem for the mixed initial boundary value problem is also proved without assuming the positive definiteness of the elastic constants.

UNIQUENESS THEOREM IN NONLOCAL THERMOELASTICITY

Abstract A theorem on the uniqueness of solution of the mixed initial-boundary ualue problem is obtained, under less restrictive conditions, in the context of the linearized isotropic nonlocal thermoelasticity theory.

UNIQUENESS IN GENERALIZED NONLOCAL THERMOELASTICITY

A work and energy equation is derived for the generalized nonlocal thermoelasticity, and it is proved that the associated initial-boundary value problem has a unique solution.

Nonlocal theory of wave propagation in thermoelastic plates

Longitudinal wave propagation in thermoelastic plates is investigated in the context of nonlocal thermoelasticity. Using the integral form of constitutive equations, balance of momenta and energy, field equations are obtained. The frequency equations are then found for symmetric and antisymmetric modes in generalized forms. To obtain tangible results, an approximate procedure is applied and numerical results are given for the case of short waves.