Showing papers on "Thermoelastic damping published in 2020"
10 Jul 2020
Abstract: In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors.
82 citations
TL;DR: In this article, analytical solutions of coupled thermoelastic forced vibrations of micro-nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory are derived.
75 citations
TL;DR: In this paper, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation, which is applied to study thermoelastic waves in a homogeneous and isotropic perfect conducting unbounded solid body containing a spherical cavity.
Abstract: In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to study thermoelastic waves in a homogeneous and isotropic perfect conducting unbounded solid body containing a spherical cavity. We use the Laplace transform method to analyze the problem. The solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The results are analyzed in different tables and graphs and compared with those obtained earlier in the contexts of some other theories of thermoelasticity.
57 citations
TL;DR: In this paper, the effect of a thermal shock loading on the rotating multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) truncated conical shells is investigated numerically according to the Lord-Shulman (L-S) thermoelastic theory.
56 citations
TL;DR: In this article, an analytical expression for the quality factor (Q) of microplate resonators is derived by applying the modified couple stress theory (MCST) considering plane stress condition and the three phase-lag (TPL) heat conduction model.
46 citations
TL;DR: In this paper, the authors present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains.
Abstract: This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate ...
46 citations
TL;DR: In this article, a robust topology optimization design for the thermoelastic composites under hybrid uncertainties of material property is investigated, where a robust objective function is formulated by a combination of average mean, average and bandwidth of standard deviation of the objective value.
43 citations
TL;DR: In this paper, the authors dealt with the small-scale effects on the thermoelastic damping (TED) in microplates and provided coupled equations of motion and heat conduction.
Abstract: This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theor...
43 citations
TL;DR: In this paper, a mathematical model of generalized thermoelasticity was proposed to investigate the transient phenomena due to the influence of the Caputo fractional derivative on generalized thermasticity.
Abstract: Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence ...
40 citations
TL;DR: In this article, a new model of three-phase-lag heat conduction of higher-order time-fractional derivatives has been derived based on fractional calculus using the approach of the Taylor series expansion of time fractional order developed by Jumarie.
Abstract: In the last few years, the theory of fractional calculus has been successfully used in thermoelasticity theories and many models of thermoelasticity with fractional order are established by several authors. In the present article, a new model of three-phase-lag thermoelastic heat conduction of higher-order time-fractional derivatives has been derived based on fractional calculus. Using the approach of the Taylor series expansion of time-fractional order developed by Jumarie (Comput Math Appl 59:1142, 2010), an alternative construction model is established extending Ezzat and others (Arch Appl Mech 82:557, 2012) and Roychoudhuri (J Therm Stress 30:231, 2007) models. This new model includes high-order time-fractional derivative approximations of three-phase-lags in the heat flux vector, the temperature gradient and in the thermal displacement gradient. We applied the resulting formulation to an infinite non-homogeneous orthotropic thermoelastic functionally graded medium having a spherical cavity with a power-law distribution of material properties along the radial direction. The effects of high-order time-fractional derivative parameters and non-homogeneity index on various distributions are discussed in detail and represented graphically and tabular forms. Finally, to illustrate the validity and accuracy of the proposed model, a comparison was made with various previous models, which are considered as special cases of our model.
40 citations
TL;DR: In this article, the constitutive relations and the governing equations for nonlocal thermoelastic solid in the presence of diffusion are derived for the free vibration of a thermo-elastic diffusive cloud.
Abstract: In this article, the constitutive relations and the governing equations are derived for nonlocal thermoelastic solid in the presence of diffusion. The free vibration of a thermoelastic diffusive cy...
TL;DR: A novel thermoelasticity model based on the Moore–Gibson–Thompson equation is considered in cases where some of these models fail to be positive, and is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source.
Abstract: Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore-Gibson-Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space-time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously.
TL;DR: In this paper, the authors presented a novel multi-single/dual-phase-lag model to investigate the thermo-elastic diffusion behavior of the medium in an isotropic half-space.
TL;DR: The vibration of the gold microbeam resonator considering the effects of the material length scale under the temperature effect is investigated in this paper, where the modified couple stress theory is applied.
Abstract: The vibration of the gold microbeam resonator considering the effects of the material length scale under the temperature effect is investigated in this article. The modified couple stress theory is...
TL;DR: The results obtained indicate a significant strong impact of FGM, TSS and laser parameters on the phenomenon, and were displayed using graphs to illustrate the extent to which non-homogeneity affected displacement, stress, temperature and strain.
Abstract: The present study utilizes the generalized thermoelasticity theory, with one thermal relaxation time (TR), to examine the thermoelastic problem of a functionally graded thin slim strip (TSS). The authors heated the plane surface bounding using a non-Gaussian laser beam with a pulse length of 2 ps. The material characteristics varied continually based on exponential functions. Moreover, the equations governing the generalized thermoelasticity for a functionally graded material (FGM) are recognized. The problem’s ideal solution was primarily obtained in the Laplace transform (LT) space. The LTs were converted numerically because of the considerable importance of the response in the transient state. For a hypothetical substance, the numerical procedures calculating the displacement, stress, temperature and strain were given. The analogous problem solution to an isotropic homogeneous material was provided by defining the parameter of non-homogeneity adequately. The obtained results were displayed using graphs to illustrate the extent to which non-homogeneity affected displacement, stress, temperature and strain. A comparison was been made between the present study and those previously obtained by others, when the new parameters vanish to show the impact of the non-homogeneity, TSS and laser parameters on the phenomenon. The results obtained indicate a significant strong impact of FGM, TSS and laser parameters.
TL;DR: In this article, a nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates.
TL;DR: In this article, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source was analyzed for generalized generalized thermo-elasticity with nonlocal effect and memory-dependent derivative.
Abstract: In the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source...
TL;DR: In this paper, the authors derived an explicit formula of the quality factor for TED based on the entropy generation approach and presented the influence of TED in the context of normalized frequency as well as beam thickness.
TL;DR: A first analysis on how the direction‐dependent Young's and shear moduli influence the flow of heat is provided, which is important for emerging heat management applications such as thermal interface and electronic packaging materials.
Abstract: Controlling thermomechanical anisotropy is important for emerging heat management applications such as thermal interface and electronic packaging materials. Whereas many studies report on thermal transport in anisotropic nanocomposite materials, a fundamental understanding of the interplay between mechanical and thermal properties is missing, due to the lack of measurements of direction-dependent mechanical properties. In this work, exceptionally coherent and transparent hybrid Bragg stacks made of strictly alternating mica-type nanosheets (synthetic hectorite) and polymer layers (polyvinylpyrrolidone) were fabricated at large scale. Distinct from ordinary nanocomposites, these stacks display long-range periodicity, which is tunable down to angstrom precision. A large thermal transport anisotropy (up to 38) is consequently observed, with the high in-plane thermal conductivity (up to 5.7 W m-1 K-1 ) exhibiting an effective medium behavior. The unique hybrid material combined with advanced characterization techniques allows correlating the full elastic tensors to the direction-dependent thermal conductivities. We, therefore, provide a first analysis on how the direction-dependent Young's and shear moduli influence the flow of heat.
TL;DR: In this paper, the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives is studied, and the equations of the heat equation are derived.
Abstract: The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. The equations of the heat ...
TL;DR: In this article, a new fractional thermo-elasticity is established by directly extending classical thermoelasticness with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana-Baleanu and Tempered-Caputo definitions.
Abstract: Fractional thermoelastic models have been formulated from classical thermoelasticity or extended thermoelasticity, i.e. Lord-Shulman or Green-Naghdi theory. It seems different authors have different physical pictures on such topic, for instance, there exist several approaches from Lord-Shulman model to fractional order ones. This work is aimed to simplify the theoretical frameworks by clarifying connections between existed models. To this end, a new fractional thermoelasticity is established by directly extending classical thermoelasticity with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana–Baleanu and Tempered-Caputo definitions. All definitions are introduced into Fourier's law by a unified way with relaxation time incorporated. Theoretically, the present model may be simplified into existed fractional theory. Numerically, it has the capability of describing thermoelastic behaviors from fractional Lord-Shulman models. For numerical studies, Laplace transform method is adopted, and a two-layered structure subjected to thermal heating is considered, from which the effects of different fractional derivatives and relaxation time are firstly uncovered. And then, the influences of material constants of two layers, especially with interfacial conditions, are discussed in detail. Finally, some concluding remarks are made.
TL;DR: In this article, an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore-Gibson-Thompson (MGT) generalized thermoelasticity theory is presented.
Abstract: Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. The finite Fourier sine transform and Laplace transform methods are used to solve the coupled thermoelastic equations. The analytical solutions are obtained for deflection and thermal moment of beams. The vibration responses of deflection and thermal moment are established in microbeams with simply supported and isothermal boundary conditions. The responses of deflection and thermal moment in beams are analyzed by comparing the results obtained under the MGT model with the corresponding results under the Lord–Shulman (LS) and Green–Naghdi (GN-III) models. The obtained results show that the amplitudes of deflection and thermal moment are attenuated, and the vibration frequency is increased due to the effect of thermoelastic coupling. It has been observed that the amplitudes of deflection under these three models are approximately the same, while the amplitude of thermal moment under the MGT model is higher than under the GN-III model and agrees with the LS model. It has been further noticed that TED depends on the size of the beams when the thermoelastic coupling effect is considered.
TL;DR: In this paper, the thermal properties of a composite cylindrical panel reinforced with graphene platelets distributed along the radial direction uniformly (UD) or functionally graded, FG − Δ, F G − ∇, F G− ∇, F g − ⋄ and F g− X pattern is studied in the frame work of elasticity theory.
Abstract: Thermoelastic behavior of composite cylindrical panel reinforced with graphene platelets distributed along the radial direction uniformly (UD) or functionally graded, F G − Δ , F G − ∇ , F G − ⋄ and F G − X pattern is studied in the frame work of elasticity theory. Functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical panel with simply supported boundary conditions is subjected to constant temperature at its inner and outer surfaces. By applying Fourier series expansion to the physical quantities along the axial and circumferential coordinates and using state space technique along the radial direction, state space governing differential equations can be derived and solved analytically. Parametric study is conducted by considering the effects of weight fraction as well as geometry and size of GPLs, pattern of graphene platelets distribution, applied temperature on thermoelastic behavior of GPLRC cylindrical panel. From numerical illustration it is evident that adding a little content GPLs affects thermoelastic behavior of GPLRC cylindrical panel significantly.
TL;DR: In this paper, a unified multi-dual-phase-lag theory is presented to study the vibration of a temperature-dependent nanobeam subjected to a ramp-type heating.
Abstract: A unified multi-dual-phase-lag thermoelasticity theory is presented to study the vibration of a temperature-dependent nanobeam subjected to a ramp-type heating. The nonlocal thermoelasticity theory based on Euler-Bernoulli hypothesis is applied. 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 present heat conduction and constitutive equations are covering at least five models of the generalized thermoelasticity. Comparison between the classical thermoelasticity (CTE), the Lord–Shulman (L–S), the Green–Lindsay (G–L), and the simple and refined-phase-lag models are made. The effects of nonlocal, ramp-type heating, and temperature-dependent parameters on all quantities have been discussed and presented graphically. It is found that the ramp-type heating parameter has significant effects on all quantities. However, the thermoelastic deflection, axial displacement, dilatation, and bending moment have strong dependencies on the nonlocal and temperature-dependent parameters.
TL;DR: This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law and its inversions have been calculated by using the Tzuo method.
Abstract: This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.
TL;DR: In this paper, the Laplace transform analysis was used to analyze the vibrations of a functionally graded thermo-piezoelectric rod of limited length, where both ends of the rod are fixed at zero voltage and are exposed to a movable axial heat source.
Abstract: In this paper, the thermoelastic vibrations of a functionally graded thermo-piezoelectric rod of limited length are considered using the generalized theory of thermoelasticity. Both ends of the rod are fixed at zero voltage and are exposed to a movable axial heat source. Using the Laplace transform analysis, the problem was solved. The expressions for the displacements, temperature, stress, electric field and electric potential were obtained. To consider the influence of the properties of gradient materials, the moving heat source velocity and thermo-piezoelectric response, some comparisons were constructed for different distributions of the physical quantities. The non-homogeneity effect on the field variables is also discussed in some detail.
Abstract: The vibration of a silver nanobeam resonator, considering the surface effect as well as the thermal effect has been investigated in this paper. The emerged bending in nanobeam resonator causes the surface effects to appear in nanobeam. The governing equations for nanobeam are obtained considering the surface and thermal effects and using the nonlocal elasticity theory. The temperature effects based on the Green–Naghdi thermoelasticity theory, and considering the thermoelastic damping, are taken into account. The vibration governing equations are derived by the coupled Green–Naghdi thermoelastic, nonlocal elasticity theory, and surface effect for Euler–Bernoulli beam model. The dynamic and temperature responses of the nanobeam are obtained in the Laplace domain using the Laplace method. The technique of inverse Laplace, called a Talbot method, is utilized to calculate the dynamic and thermal responses of the nanobeam in the time domain. To investigate the results, the effects of the various parameters, such as the surface effects, nonlocal parameter, and the initial temperature conditions, on the dynamic and temperature responses of the microbeam are scrutinized.
TL;DR: In this article, the non-local behavior during thermal lagging is studied to accommodate the effect of the thermomass for a piezoelastic half-space due to the influence of magnetic field in the nonlocal behavior.
Abstract: In the present analysis, the non-local behavior during thermal lagging is studied to accommodate the effect of the thermomass for a piezoelastic half-space due to the influence of magnetic field in...
TL;DR: In this paper, an analytical formula of TED in micro/nanobeam resonators with circular cross-section was developed, and the series-form type of DPL-TED model was also proposed and compared with the modified existing model.