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The objective of this manuscript is to examine the thermodynamical disturbances in a rotating nonlocal transversely isotropic thermoelastic solid half-space. The enunciation is applied to Lord–Shulman model of generalized thermoelasticity with Eringen's nonlocal elasticity theory. The formulation is subjected to a mechanical load. The expressions for the displacement components, stresses and temperature field are obtained by using normal mode technique and the numerical computations have been carried out with the help of MATLAB software for zinc crystal-like material. The comparisons are made among the results obtained by taking into account the different values of rotation parameter $ (\Omega =0.0, 0.1, 0.3) $ (Ω = 0.0 , 0.1 , 0.3) , nonlocal parameter $ (\varepsilon =0.195\times 10^{-9}, 0.195\times 10^{-4}, $ (ε = 0.195 × 10 − 9 , 0.195 × 10 − 4 , $ 0.195\times 10^{-1}) $ 0.195 × 10 − 1) and time $ (t=0.1, 0.3, 0.5) $ (t = 0.1 , 0.3 , 0.5). The outcomes point out a strong impact of the rotation, nonlocality and time on the physical quantities and agree with the boundary conditions. Although various studies exist in the literature for local and isotropic thermoelastic medium, but the current results are presented in an anisotropic and nonlocal thermoelastic rotating medium, which have not been studied so far. [ABSTRACT FROM AUTHOR]

The present article is concerned with the reflection of plane harmonic waves in a nonlocal micropolar thermoelastic medium having void pores in the context of dual-phase-lag and Lord-Shulman models. Two sets of coupled shear waves and three sets of coupled longitudinal waves are shown to exist. When a coupled longitudinal displacement wave is made incident, the reflection coefficients of the various reflected waves and their respective energy ratios are computed analytically and the numerical computation is carried out with the help of MATLAB software. For a particular model, the influence of nonlocal, voids and micropolar parameters on the variations of reflection coefficients and energy ratios of various reflected waves is presented graphically. It is verified that during reflection phenomenon, the sum of energy ratios is equal to unity at each angle of incidence. A comparison between the dual-phase-lag model and Lord-Shulman model is also depicted graphically. [ABSTRACT FROM AUTHOR]

The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion theory. The main aim is to establish a size-dependent model with the consideration of spatial nonlocal effects of concentration and strain fields. The heat transport equation for the present problem is considered in the context of Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory involving linear and nonlinear kernel functions in a delayed interval in terms of the memory-dependent derivative. The medium is considered to be one-dimensional having a spherical cavity where the boundary of the cavity is traction-free and is subjected to prescribed thermal and chemical shocks. The Laplace transform technique is incorporated for the solution of the basic equations. For numerical evaluation, the analytical expressions have been inverted in the space-time domain using the method of Zakian. From numerical results, the effects of the nonlocality parameters in the heat transport law and the nonlocality of mass-flux have been discussed. The effect of different kernel functions, the delay time, and the effect of thermodiffusion are also reported. A comparative study between the MGT theory and the hyperbolic Lord–Shulman theory is also explained. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the current manuscript is to investigate the reflection of plane waves in a rotating, two-dimensional homogeneous, initially stressed, nonlocal orthotropic thermoelastic solid half-space based on dual-phase-lag model. Design/methodology/approach: The reflection phenomenon has been utilized to study the effects of initial stress, rotation and nonlocal parameter on the amplitude ratios. During the reflection phenomenon three coupled waves, namely quasi displacement primary wave (qP), quasi thermal wave (qT) and quasi displacement secondary wave (qSV) have been observed in the medium, propagating with distinct velocities. After imposing the suitable boundary conditions, amplitude and energy ratios of the reflected waves are obtained in explicit form. Findings: With the support of MATLAB programming, the amplitude ratios and energy ratios are plotted graphically to display the effects of rotation, initial stress and nonlocal parameters. Moreover, the impact of anisotropy and phase lags is also observed on the reflection coefficients of the propagating waves. Originality/value: In the current work, we have considered rotation and nonlocality parameters in an initially stressed orthotropic thermoelastic half-space, which is lacking in the published literature in this field. The introduction of these parameters in a nonlocal orthotropic thermoelastic medium provides a more realistic model for these studies. The present work is valuable for the analysis of orthotropic thermoelastic problems involving rotation, initial stress and nonlocality parameters. [ABSTRACT FROM AUTHOR]

The model of nonlocal thermoelasticity is applied on a half-space overlaid by a thick layer of different materials, depending on generalized thermoelasticity theories (L. S). To solve this problem we take the upper surface is to be traction-free and is subjected to a constant thermal shock. The analytical expressions for temperature, displacement, and stresses were obtained by using the Laplace transform technique. Besides, comparisons are presented in graphs to illustrate the effects of different factors. [ABSTRACT FROM AUTHOR]

Current research is dedicated to study the influence of angular velocity and gravity field on the thermomechanical interactions in a non-homogeneous, nonlocal, micropolar elastic half-space whose surface is subjected to a mechanical load. The formulation is established in the context of dual-phase-lag model of generalized thermoelasticity. The material is supposed to have non-homogeneous thermoelastic properties in the x-direction. Exact solution of the problem is procured by applying normal mode technique. Numerical computations for nonlocal stresses, displacement components and temperature field are performed for a suitable material and are depicted graphically. Certain special cases of interest have been derived from the current report. [ABSTRACT FROM AUTHOR]

Purpose: The current manuscript is devoted to scrutinize the effects of nonlocal parameter, internal heat source, and initial stress on the interactions caused by a moving thermal load in a generalized thermoelastic solid half-space. Methods: The medium is assumed to be initially stressed and has uniform temperature. The problem has been modeled by employing the modified Green–Lindsay theory to carry out the investigation.The governing equations are handled with an analytical–numerical technique based on normal mode. In this technique, one gets exact solution without any assumed restrictions on the field variables. The normal mode technique is applicable to a wide range of problems in thermodynamics and thermoelasticity. Results and Conclusions: Expressions for displacement, stresses, and temperature in the physical domain are obtained. The problem is illustrated by computing the numerical values of the field variables for a copper like material. Comparisons of the physical quantities are shown in figures to study the effects of nonlocal parameter, internal heat source, initial stress, and velocity of the thermal load. Some particular cases of interest have also been inferred from the present problem. Originality/Value: In this article, we have investigated the effects of nonlocal parameter, internal heat source, initial stress, and velocity of the thermal load on the thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, but the work in its present form, i.e., the disturbances in a thermoelastic medium in the presence of initial stress, nonlocal effect, and internal heat source under modified Green–Lindsay model have not been studied till now. The present work is useful and valuable for the analysis of problems at nanoscale level involving moving heat source, initial stress, and elastic deformation. [ABSTRACT FROM AUTHOR]

Purpose: The impact of gravity on nonlocal thermoelastic diffusion solid is discussed in this work. Methods: The Green-Naghdi theory (G-N II), the Lord-Shulman theory, and the three-phase-lag model all explore the issue. The governing equations are solved using the normal mode technique to get the analytic forms of the displacements, temperatures, force stress tensors, and mass concentration. Using appropriate boundary conditions, the physical fields are calculated and the numerical computations have been carried out with the help of MATLAB programming. Results: In the physical domain, numerical results for the field quantities are provided and graphically displayed in both the absence and presence of gravity and the nonlocal parameter. Conclusion: Physical variables are affected by nonlocal thermoelasticity as well as the gravity field. [ABSTRACT FROM AUTHOR]

In this paper, we explore the application of nonlocal theory to analyze the phenomenon of coupled thermoelastic wave reflection in a semiconducting diffusive medium, considering its temperature rate dependence. The governing equations are deconstructed using the Helmholtz vector rule, allowing us to delve into the behavior of the system. By calculating the dispersion relation in terms of propagation speed, we investigate four coupled longitudinal waves alongside an independent nondispersive transverse wave within the local medium. The cut-off frequencies for each wave are discussed, shedding light on their characteristics. Furthermore, we delve into the phenomenon of coupled longitudinal displacement waves at the medium’s boundary. Analytical derivations of amplitude ratios are presented, accompanied by graphical representations of their behavior, focusing on a semiconductor material such as copper. We examine the effects of physical parameters, including the nonlocal and diffusive parameters, on the obtained results. It is important to note that the existing literature primarily lacks consideration of diffusivity and plasma transportation. Lastly, we validate our findings by investigating the conservation of energy within the system. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the thermoelastic interactions in a nonlocal initially stressed fiber-reinforced transversely isotropic half-space with microtemperatures. The formulation is established in the context of Green-Naghdi theory of thermoelasticity without energy dissipation. Normal mode technique is used to obtain the general solution for a set of boundary conditions. The expressions of different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain and numerical computations are carried out with the help of MATLAB software. Comparisons are made among the results for different values of nonlocal parameter and time along with the results obtained in the presence and absence of fiber-reinforcement and microtemperature. The outcomes point out a strong impact of the nonlocal parameter, fiber-reinforcement, microtemperatures and time on the field variables. Some particular cases of special interest have also been deduced to show the comparison between the present results and previous investigations. [ABSTRACT FROM AUTHOR]

The term "optical thermoelasticity" is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters. [ABSTRACT FROM AUTHOR]

Thermoelastic modeling at nanoscale is becoming more important as devices shrink and heat sources are more widely used in modern industries, such as nanoelectromechanical systems. However, the conventional thermoelastic theories are no longer applicable in high-temperature settings. This study provides an insight into the thermomechanical features of a nonlocal viscous half-space exposed to a cyclic heat source. Using a novel concept of fractional derivatives, introduced by Atangana and Baleanu, it is assumed that the viscoelastic properties follow the fractional Kelvin–Voigt model. The nonlocal differential form of Eringen's nonlocal theory is employed to consider the impact of small-scale behavior. It is also proposed that the rule of dual-phase thermal conductivity can be generalized to thermoelastic materials to include the higher-order time derivatives. The numerical results for the examined physical variables are presented using the Laplace transform technique. Furthermore, several numerical analyses are performed in-depth, focusing on the effects of nonlocality, structural viscoelastic indicator, fractional order, higher-order and phase-lag parameters on the behavior of the nanoscale half-space. According to the presented findings, it appears that the higher-order terms have a major impact on reactions and may work to mitigate the impact of thermal diffusion. Furthermore, these terms provide a novel approach to categorize the materials based on their thermal conductivities. [ABSTRACT FROM AUTHOR]

The present article deals with thermoelastic boundary value problem in three-dimensional orthotropic medium based on Eringen's nonlocal elasticity. A time-dependent thermal shock is applied on the traction-free surface of homogeneous orthotropic solid and the problem is treated in the context of Green-Naghdi model type III. The governing equations of three-dimensional problem of generalized thermoelasticity are obtained as a vector matrix differential equation form by employing normal mode analysis to the considered equations which are then solved by eigenvalue approach. The effect of nonlocal parameter on the displacements and temperature are presented graphically. [ABSTRACT FROM AUTHOR]

The generalized nonlocal thermoelastic model in the context of Eringen's nonlocal elasticity is applied to investigate the magnetothermoelastic interactions in a rod of finite length placed in a magnetic field with a moving source. With the use of the Laplace transform and numerical Laplace inversion techniques, the governing equations are solved, and the solutions in the time domain are obtained numerically. The distributions of the nonlocal thermal stress, temperature, and the displacement in the rod are obtained and presented graphically. The effects of the rotational speed and the speed of the moving heat source, nonlocal parameter, and the applied magnetic field intensity on the considered variables are discussed in detail. [ABSTRACT FROM AUTHOR]

The term “optical thermoelasticity” is used to describe how the optical properties of a material change when it is heated or deformed mechanically. The issues of effective elastic and heat transfer symmetry are given particular focus. This study gives a new nonlocal theoretical formulation for a thermo-optical elastic material that can be used to describe how thermomechanical waves and plasma waves relate to the symmetry of semiconductor materials such as silicon or germanium. The suggested model includes the idea of nonlocal elasticity and a modified Moore–Gibson–Thompson (MGT) heat conduction equation with nonsingular fractional derivative operators. The heat transfer equation has been converted and generalized into a nonsingular fractional form based on the concepts of Atangana and Baleanu (AB) using the Mittag–Leffler kernel. The developed model is used to examine the effect of thermal loading by ramp-type heating on a free plane of unbounded semiconductor material symmetries. Using the Laplace transform approach, we may analytically obtain linear solutions for the investigated thermo-photo-elastic fields, such as temperature. The Discussion section includes a set of graphs that were generated using Mathematica to evaluate the impact of the essential parameters.

This study treats a new model of nonlocal fractal thermoelasticity beam theory for nanomaterials characterized by an apparent negative thermal conductivity which occurs in shaped graded materials. The model is based on the new concept of "product-like fractal measure" introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media with fractal dimension α. The basic setups of the theory are formulated, yet, we have restricted our analysis for the static case. The effects of fractal dimension on field variables, in particular the lateral deflection and the temperature increment of the resonator were analyzed analytically and graphically. It was observed that the physics of the thin elastic nanobeam is affected by the numerical value of the fractal dimension and the characteristic lengths of the theory. Comparable scenarios observed in complex material structures are obtained and discussed. [ABSTRACT FROM AUTHOR]

The present work introduces the thermoelastic vibrations of nonlocal nanobeams resting on a two-parameter foundation. The governing equations are formulated for linear Winkler–Pasternak foundation type based on the generalized dual-phase-lag heat conduction and nonlocal beams theories. The nanobeam is subjected to a temperature ramping function. The coupled equations of the problem are formulated and solved by Laplace transform technique. The effects of the nonlocal parameter and different foundation parameters on the field variables are illustrated graphically and discussed. The results obtained are consistent with previous analytical and numerical results.

The present paper deals with the propagation of surface waves in an isotropic and homogeneous nonlocal generalized thermoelastic solid half-space with voids. The dispersion relations for Rayleigh-type surface wave are derived for both thermally insulated and isothermal boundaries. The non-dimensional wave speed of Rayleigh-type surface wave is computed for some specific constants of a material representing the present model. The dependence of non-dimensional wave speed on frequency, nonlocality, thermal and voids parameters is illustrated graphically. [ABSTRACT FROM AUTHOR]

Thermoelastic modeling at nanoscale is becoming more important as devices shrink and heat sources are more widely used in modern industries, such as nanoelectromechanical systems. However, the conventional thermoelastic theories are no longer applicable in high-temperature settings. This study provides an insight into the thermomechanical features of a nonlocal viscous half-space exposed to a cyclic heat source. Using a novel concept of fractional derivatives, introduced by Atangana and Baleanu, it is assumed that the viscoelastic properties follow the fractional Kelvin–Voigt model. The nonlocal differential form of Eringen’s nonlocal theory is employed to consider the impact of small-scale behavior. It is also proposed that the rule of dual-phase thermal conductivity can be generalized to thermoelastic materials to include the higher-order time derivatives. The numerical results for the examined physical variables are presented using the Laplace transform technique. Furthermore, several numerical analyses are performed in-depth, focusing on the effects of nonlocality, structural viscoelastic indicator, fractional order, higher-order and phase-lag parameters on the behavior of the nanoscale half-space. According to the presented findings, it appears that the higher-order terms have a major impact on reactions and may work to mitigate the impact of thermal diffusion. Furthermore, these terms provide a novel approach to categorize the materials based on their thermal conductivities.

The thermoelastic analysis is extremely important due to the highly integrated characteristics in micro- and nano-electro-mechanical systems. In this paper, thermal flux driven (TFD) and temperature gradient driven (TGD) two-phase local/nonlocal heat conduction integral models (NHCIM) are developed to describe size-dependent heat conduction. Combining TFD- and TGD-NHCIMs with strain- and stress-driven two-phase local/nonlocal elastic integral models, four types of nonlocal thermoelastic integral models are developed to predict the thermoelastic behavior of microstructures. The nonlocal thermoelastic integral models are applied to analyze the thermoelastic behavior of clamped-clamped microrod with prescribed boundary temperature and heat flux for each end. Analytical solutions for the distribution of temperature, displacement and thermal stresses are derived and expressed explicitly with several unknown constants, which can be determined by the standard and constitutive boundary conditions. The effects of nonlocal parameters on the distribution of temperature, displacement and thermal stress are investigated numerically and systematically. The numerical results show that nonlocal thermoelastic models based on the combination between strain- and stress-driven two-phase local/nonlocal elastic models respectively with TGD- and TFD-NHCIMs would lead to consistent size-dependent response when increasing the elastic and thermal nonlocal length-scale parameters at the same time, while those based on the combination between strain- and stress-driven two-phase nonlocal elastic models respectively with TFD- and TGD-NHCIMs would lead to inconsistent prediction. [ABSTRACT FROM AUTHOR]

In this work, a three‐dimensional model of the generalized thermoelasticity with fractional order stain and nonlocal effect is established. Nonlocal effect is used to depict size‐dependence feature and fractional order strain is considered to describe memory‐dependence properties. The Laplace and double Fourier transform techniques are applied to the three‐dimensional half‐space model subjected to thermal shock and traction free surface. A complex inversion formula of the transform with the techniques of the Fourier expansion been applied to obtain the inverses of double Fourier transforms, and Laplace transforms. Numerical results for the temperature, stress, strain and displacement are represented graphically based on various values of the fractional order strain parameter and elastic nonlocal parameter. The fractional order strain and nonlocal parameter has a limited effect on the thermal waves while it has significant effects on the mechanical waves. [ABSTRACT FROM AUTHOR]

• Coupled photo-thermoelasticity analysis is carried out for a semiconducting micro/nano beam resonator. • An analytical method based on Green-Naghdi theory is employed for the analysis. • The assumed semiconducting micro/nano beam resonator is subjected to shock loadings. • The transient behaviours of carrier density field are studied. • The small scale effects are taken into account employing Eringen nonlocal theory. In this article, coupled photo-thermoelasticity analysis is carried out using an analytical method in a semiconducting micro/nano beam resonator, considering Green – Naghdi theory (with energy dissipation) and small scale effects. The governing equations for temperature and displacement fields are derived using Eringen nonlocal theory combined with Rayleigh beam theory. One end of the assumed semiconducting MEMS/NEMS is excited by three types of suddenly increasing carrier density and temperature as the plasma and thermal shock loading. The transient behaviours of carrier density field are studied and the effects of disturbances in plasma field on other fields including temperature and deflection are obtained using the proposed analytical solution. The presented analytical solution is based on Laplace transform. To find the dynamic and transient behaviours of fields' variables in time domain, an inversion Laplace technique is utilized, which is called Talbot method. The effects of small scale parameter and dimensions of the semiconducting micro/nano beam on the dynamic behaviours of fields' variables are discussed in detail. The axial wave propagation and the distribution of fields' variables along axial direction are studied at various times. [ABSTRACT FROM AUTHOR]

In this paper, a new model based on Eringen's nonlocal thermoelasticity is constructed. The propagation of Rayleigh surface waves in homogeneous isotropic medium is considered under the purview of this new nonlocal thermoelasticity theory in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach. The frequency equations for different cases are derived. The phase velocity, attenuation coefficients, specific loss and penetration depth of Rayleigh surface waves are computed numerically and presented graphically with respect to frequency and the effects of non-locality on the considered parameters are presented in the figures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work produces a new model of nonlocal thermoelastic nanobeams of temperature-dependent physical properties. A nanobeam is excited by harmonically varying heat and subjected to an exponential decaying time varying load. The analytical solution is obtained by means of Laplace transform method in time domain. Inversions of transformed solutions have been preceded by using calculus of residues. Effects of nonlocal parameter, variability thermal conductivity, varying load and angular frequency of thermal vibration on studied fields of nanobeam are investigated and discussed. [ABSTRACT FROM AUTHOR]

The paper deals with the mechanics of nanobeams within nonisothermal environments. Mechanical behaviour is assumed to be time-independent and suitable for the statical beam deformation. The nanobeam mechanics is based on the Timoshenko kinematics, augmented by nonlocality effects as advocated by Eringen. Following a thermodynamic approach, a sound framework oriented toward anisotropic materials is developed. Such nanobeam model is especially suited for functionally graded materials. The proposed procedure is tested on two examples. The first example investigates mechanical behaviour in the more general way for the different temperature distributions, while the second one is oriented toward specific carbon nanotube – Poly(methyl methacrylate) nanocomposite. [ABSTRACT FROM AUTHOR]

The Bernoulli–Euler beam formulation is extended by means of the nonlocal strain gradient theory in the nonhomogenous temperature field setting. Starting from the nonlocal continuum mechanics, a thermodynamically consistent model is obtained. The governing higher order system of differential equations for axial and transverse displacements is presented. Utilization of boundary conditions is demonstrated on four examples. It can be concluded that the nonhomogenous temperature field has a profound influence on the nanobeam mechanics. Some conclusions are drawn at the end of the paper. [ABSTRACT FROM AUTHOR]

In this work, a model of nonlocal generalized thermoelasticity with one thermal relaxation time is used to consider the vibration behavior of an Euler-Bernoulli (E-B) nanobeam. The thermal conductivity of the nanobeam is assumed to be temperature-dependent. The nonlocality brings in an internal length scale in the formulation and, thus, allows for the interpretation of size effects. The governing partial differential equations are solved in the Laplace transform domain by adopting the state-space approach of modern control theory. The inverse of Laplace transforms are numerically computed using Fourier expansion techniques. The distributions of the lateral vibration, the temperature, the axial displacement and the bending moment of the nanobeam are determined. The effect of thickness and variability of thermal conductivity, as well as the influence of the nonlocal parameter are investigated. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

The investigation for propagation and reflection of plane waves is carried out based on three-phase-lag (TPL) thermoelasticity with the aids of Eringen's nonlocal theory in a special medium - biological tissue. The scalar and vector potential functions of Helmhotz decomposition are adopted to obtain the propagation speeds, attenuation coefficients and reflection coefficients of plane waves analytically. There are two sets of dispersive attenuated longitudinal waves whose speeds of propagation are associated with angular frequency, and independent transverse elastic shear wave which exhibits no attenuation. It is found that the blood perfusion rate has few effects on wave propagation speed and attenuation coefficient and the phase lag of temperature gradient is negligible in present configuration. The effects of working angular frequency, nonlocal parameters, phase lag times, reflecting thermal boundaries and the type of incident waves on the propagation speeds, attenuation coefficients and reflection coefficients of harmonic waves are discussed and investigated graphically. [ABSTRACT FROM AUTHOR]

An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales. [ABSTRACT FROM AUTHOR]