Effect Of Thermoelastic Coupling Research Articles

Event-Triggered Control for a Second Order ODE-Heat System Coupling at Intermediate Point

Motivated by the thermoelastic coupling effect arising in microelectromechanical systems (MEMS), event-triggered control of second-order ODE-heat systems coupled at intermediate point is investigated. The event-triggered control includes two parts, one is the feedback control signal, and the other is the event-triggered mechanism that decides when to update the control input. First, we design an event-triggered controller by using Zero-Order Hold to a continuous-time controller. Then, a dynamic triggering condition is established. Next, we derive that the existence of a minimal dwell-time, which avoids the occurrence of Zeno behavior. By utilizing Lyapunov-Krasovskii functional method, the global exponential stability of the closed-loop system is demonstrated. Finally, the simulation data based on the thermoelastic coupling system is displayed to demonstrate the availability of the theoretical results.

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

A coupled thermoelastic model with fractional order derivative which incorporates the microstructural effects and thermoelastic coupling effects simultaneously at small scale is provided and is used to study wave dispersion and bandgap features of Bloch waves in one-dimensional phononic crystals. Dipolar gradient elasticity is used to account for the effects of microstructure while the non-Fourier heat conduction with fractional order derivatives is used to model thermal conduction at small scale. The interaction of thermo-elastic coupled waves with a periodic structure leads to Bloch waves, and the transfer matrix method is used to obtain the dispersion equation of the Bloch waves based on the Bloch theorem. A parameter study is performed in the numerical example to investigate the influence of the strain gradient parameter, the micro-inertial parameter, the relaxation time and the fractional order on the dispersion and bandgap of Bloch waves.

Elastic and thermal effects upon the propagation of waves with assigned wavelength

It is well known that harmonic longitudinal elastic waves propagate without damping in time, while the heat equation leads to standing modes that decrease exponentially over time. In this article, it is shown that the elastic deformation when coupled with thermal deformation leads to the following effects on the propagation of harmonic longitudinal waves and on standing modes: (a) the harmonic longitudinal waves become damped in time; (b) the standing modes suffer a slower decrease in time in relation to the pure thermal modes; and (c) the propagation speed of harmonic longitudinal waves increases in relation to that predicted by the purely elastic theory. The dependence of the dimensionless parameters that characterize the effects described at these previous points in relation to the material and coupling characteristics is explicitly presented and then is numerically simulated and graphically illustrated. As regards the Rayleigh waves class, although a rigorous mathematical proof is not offered, the numerical results presented for a lot of common thermoelastic materials show the same effects of thermoelastic coupling as in the case of longitudinal harmonic plane waves. The present article systematically synthesizes the thermal effects on wave propagation, and it provides a reference work with regard to the thermoelastic coupling.

Flexural waves in thermoelastic higher-order shear micro-plate modelled by spatiotemporal fractional differential

An orthotropic higher-order shear micro-plate model is established with consideration the small-scale effect and the thermoelastic coupling effects to study the dispersion and attenuation of flexural waves in the present work. The nonlocal elasticity and the strain gradient elasticity are incorporated to lead the nonlocal strain gradient model to reflect the size effect. The generalized thermoelasticity (non-Fourier heat conduction) is introduced to reflect the history-dependent feature of heat conduction. Furthermore, the integer order derivatives are replaced by the fractional derivatives of Caputo-type to get a more refined model which can extend the range of application of model and provide more exquisite description of the spatial nonlocal behavior and temporal memory behavior at small scale. In addition, the nonlocal characteristic length and the memory characteristic length as new small scale parameters are first introduced in the present model to focus on describing the short-range nonlocal and the short-term memory behavior. A detailed parameter study is performed and the effects of nonlocal characteristic length, strain gradient characteristic length, the memory characteristic length and the spatiotemporal fractional order on the dispersion and attenuation of thermoelastic coupled flexural waves are discussed based on the numerical results.

Thermoelastic damping analysis in nanobeam resonators considering thermal relaxation and surface effect based on the nonlocal strain gradient theory

With the extensive applications of the micro/nano-electro-mechanical systems, a great deal of attention has been paid to explore the influences of the arising size-dependent effect and surface effect on their performance. Along with these effects, the nonlocal elasticity, strain gradient theory, and surface elasticity theory were successively proposed. Moreover, it is inevitable for MEMS/NEMS to work in a variable temperature environment, correspondingly, the thermal-induced stress or deformation becomes another issue that needs serious concern. Thermoelastic damping (TED), as a main energy dissipation source, is a major challenge in designing higher-quality factor resonators. However, considering the thermoelastic coupling effect, the aforementioned theories are not capable enough to depict the thermoelastic performance of micro/nano-resonators. To amend this deficiency, based on nonlocal strain gradient theory, a new model for assessing the TED of nanobeam resonators by incorporating the thermal relaxation effect and the surface effect is developed. The corresponding governing equations for the Euler–Bernoulli microbeam resonator model are formulated, and then, solved by means of a complex frequency method. The influences of the nonlocal parameter, strain gradient coefficients, aspect ratio, surface stress and surface elasticity on the TED are examined and discussed in detail.

Thermoelastic coupling vibration analysis of precision coated TPU film

TPU (thermoplastic polyurethane) films are subjected to heating in production. As the temperature rises, thermal stress will be generated inside the TPU film. It causes defects, such as wrinkles and cracks, in the moving TPU film; therefore, it is of great significance to study the thermoelastic coupling effect of the moving TPU film in the printing process. To study the thermoelastic coupling vibration characteristics of the moving TPU film under the opposite edge tension, it includes combining the thermal conduction equation with temperature coupling term and the vibration differential equation with variable temperature effect to get the coupling equation. The differential quadrature method is used to discretize the vibration differential equation. The influence of the thermoelastic coupling coefficient, aspect ratio, and tension ratio on the vibration characteristics of the TPU film is studied.

Atomistic investigation on the conversion of plastic work to heat in high-rate shear deformation

The conversion of work into heat is one of the most significant characteristics of plastic deformation, especially in a high strain rate regime. The quantitative characterization of the fraction of plastic work converted into heat plays a crucial role in understanding the deformation process and mechanism and establishing an accurate and reasonable thermomechanical constitutive model. However, the fraction of plastic work converted into heat is experimentally found to span over a wide range of values between 0.1 and 1. In this paper, the conversion of plastic work into heat in high-rate shear deformation is systematically investigated through the relations between temperatures, stresses, elastic and plastic strains using molecular dynamics simulation. The results show that the temperature rise in the shear deformation is caused by the heat dissipation of the plastic work rather than the thermo-elastic coupling effect due to invariance of the volume. Dislocation nucleation and glide are the main mechanisms of shear deformation and are also the origins of heat generation. The continuous slip of dislocations also results in the formation of deformation twins. Interestingly, the work-to-heat conversion coefficient is revealed to be independent of crystal orientation, in contrast to the plastic deformation itself. From the present study, we conclude that almost all the plastic work in shear deformation is converted into heat dissipation for all studied samples.

Frequency shifts and thermoelastic damping in different types of Nano-/Micro-scale beams with sandiness and voids under three thermoelasticity theories

The present work focuses on the analytical study of thermoelastic damping (TED) and frequency shift (FS) in micro-scale beams and TED in nano-scale beams. The considered thermoelastic beam is homogeneous, isotropic, and consists of sandiness and voids (TESV). TED and FS of the beam are studied under four types of distinct boundary conditions, viz. clamped-clamped (CC), simply supported-simply supported (SS), Cantilever, and clamped-simply supported (CSS), considering different types of practical engineering applications. Newton–Raphson method is used to numerically evaluate the first two eigenvalues of each type of beam. The expressions of the characteristic roots are also provided. Based on the linear Euler–Bernoulli theory, the closed-form expressions for the beams’ transverse vibrations are derived. Analytical expressions for the deflection, change in temperature, and void volume fraction are also obtained, followed by TED and FS analysis for the considered boundaries. Three theories of thermoelasticity, viz. the Classical dynamical coupled (CL), Lord–Shulman (LS), and Green–Lindsay (GL) thermoelasticity theories are considered in this problem. The influences of thermal relaxation times owing to the three thermoelasticity theories, voids, sandiness, micro & nano dimensions of the beam, and the first two modes (M1 & M2) on the TED and FS are illustrated graphically. Critical thickness (CrTh) and critical length (CrLt) of all four beams under the influence of the existing parameters are meticulously analyzed. Some special cases of this problem are discussed, and the obtained outcomes are validated with well-established results found in the extant literature. In-depth analysis of the effects of thermoelastic coupling and other existing parameters on the natural frequency of micro-/nano-scale resonators, among other applications, is quintessential for designing and optimizing frequency-sensitive nanoelectromechanical systems (NEMS) and microelectromechanical systems (MEMS). Hence, the present analysis may have significant application and contribution in areas utilizing NEMS/MEMS devices.

Reflection of thermoelastic coupled plane waves under the MGL model

The present study is concerned with the reflection phenomenon of thermoelastic plane waves at the thermally insulated stress-free surface of a homogeneous isotropic thermally conducting elastic half-space in the frame of modified Green-Lindasy (MGL) model of generalized thermoelasticity with strain rate. The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive in nature as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exist one independent vertically shear-type (SV-type) wave. In contrast to the classical Green-Lindsay (GL) and the Lord-Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on a surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs are plotted to analyzed the analytical solution. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the MGL model with those obtained in case of the GL, LS and the coupled thermoelasticity (CTE) models.

Investigation of Thermoelastic Wave Propagation in Euler–Bernoulli Beam via Nonlocal Strain Gradient Elasticity and G-N Theory

The size-dependent effect arising in micro/nano-structures has attracted considerable attention in academic and industrial communities. The theories developed to characterize such effect mainly include the nonlocal elasticity theory, the strain gradient theory, the modified coupled stress theory and the more recent nonlocal strain gradient elasticity etc. Meanwhile, the thermal-induced deformation or stress in micro/nano-structures is increasingly becoming a vital issue in their designs and applications. Nevertheless, theoretical investigations to predict the thermoelastic performances of micro/nano-structures are not so common, especially in the case of nonlocal strain gradient elasticity incorporating thermoelastic coupling effect. In present work, investigation of thermoelastic wave propagation in micro-beam is conducted in the context of the nonlocal strain gradient elasticity and the G-N theory, taking the thermoelastic coupling effect into account. The governing equations are formulated based on the Euler–Bernoulli beam model and the G-N theory. By assuming the wave-type solutions, the equations are solved and the dispersion relation between frequency and wave number and the relation between phase velocity and wave number are determined respectively. In calculation, the above two relations are fully investigated and comparisons on them under different theories are provided accordingly. Some new findings are presented and discussed in detail. It is hoped that the present work may provide some guidelines in designing and optimizing micro-structures.

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

AbstractThe present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

Nonlinear superharmonic and subharmonic resonances of piezoelectric elliptic thin plates under thermoelastic coupling effect

This paper aims at investigating the nonlinear vibration characteristics of the piezoelectric elliptic thin plate under the combined action of external harmonic excitation and temperature field. Based on the Von-Karman plate theory of large deflection, the nonlinear governing equation is derived by using the Bubnov-Galerkin method. Then, the amplitude-frequency response equations are further obtained using the multi-scale method, and the stability conditions of the steady solution are determined according to the Routh-Hurwitz criterion. The effects of the temperature difference at the plate center, the effective damping coefficient, the external excitation amplitude, and the ratio of the semi-major axis to the semi-minor axis on superharmonic and subharmonic resonances behaviors of the piezoelectric elliptic thin plate are analyzed. It is found that the coexistence region of multiple solutions and the resonant amplitude decrease for superharmonic resonance, as the temperature difference at the plate center increases. For subharmonic resonance, with the increase in the temperature difference at the plate center, the response amplitude increases, while the distance between two branches of the amplitude-frequency response curve has no obvious change. The softened/hardened nonlinear characteristics of the system are determined by the ratio of the semi-major axis to the semi-minor axis of the piezoelectric elliptic thin plate.

Reflection of magneto-thermoelastic waves at a solid half-space under modified Green–Lindsay model with two temperatures

The present study is concerned with the reflection of magneto-thermoelastic plane waves from stress free and thermally insulated surface in a homogeneous isotropic thermally conducting elastic half-space medium. The modified Green–Lindsay (MGL) theory of generalized thermoelasticity has employed with two temperatures (2 T). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. There exist also due to the thermoelastic coupling one independent vertically shear (SV-wave) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the reflection coefficients and their respective energy ratios for reflected thermoelastic waves have been determined when the coupled longitudinal wave incident on the free surface. A numerical result on the reflection coefficients and their respective energy ratios for the specific parameter has been calculated. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those in the classical GL model.

Thermoelastic damping analysis in microbeam resonators based on Moore–Gibson–Thompson generalized thermoelasticity theory

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.

Waves in magneto-thermoelastic solids under modified Green–Lindsay model

In this paper, the propagation of time-harmonic plane waves is investigated in an infinite elastic solid material by employing the modified Green–Lindsay (MGL) model of generalized thermoelasticity. It is found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type (SV-type) wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the thermoelastic coupling effect. In contrast to the Green–Lindsay (GL) as well as the Lord–Shulman (LS) models, the SV-type wave is not only dispersive in nature but also experiences attenuation. Reflection phenomenon of an incident coupled longitudinal wave from stress-free and thermally insulated boundary surface of a thermoelastic solid half-space is addressed. Using these boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, reflection coefficients and their respective energy ratios. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in the case of the GL model.

Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping

This paper presents a theoretical investigation on the response of free vibration of functionally graded material (FGM) micro-plates with thermoelastic damping (TED). Continuous through thickness variation of the mechanical and thermal properties of the FGM plate is considered. By employing the simplified one-way coupled heat conduction equation and Kirchhoff’s plate theory, governing equations for the free vibration of the FGM micro-plates with thermoelastic coupling effect are established, in which stretching-bending coupling produced by the material inhomogeneity in the thickness direction is also considered. The heat conduction equation with variable coefficients is solved effectively by a layer-wise homogenization approach. Harmonic responses of the FGM micro-plates with complex frequency are obtained from the mathematical similarity between the eigenvalue problems of the FGM micro-plate with TED and that of the homogenous one without TED. The presented analytical solutions are suitable for evaluating TED in FGM micro-plates with arbitrary through-thickness material gradient, geometry and boundary conditions. Numerical results of TED for a ceramic-metal composite FGM micro-plate with power-law material gradient profile are illustrated to quantitatively show the effects of the material gradient index, the plate thickness, and the boundary conditions on the TED. The results indicate that by adjusting the physical and geometrical parameters of the FGM micro- plate, one can get the minimum of the TED which is even smaller than that of the pure ceramic resonator.

The analyses of dynamic response and reliability for failure-dependent stochastic micro-resonator with thermoelastic coupling effects

A crucial measure for the design of high-performance micro-resonators is to consider the randomness of structural parameters when analyzing the structural system reliability. In this work, the stochastic dynamic response analysis and subsequently, a dynamic reliability assessment of the random micro-resonators are originally presented, where the thermoelastic coupling effects are freshly incorporated in the models proposed. The dynamic characteristics equation of the deterministic micro-resonator is firstly established based on the finite element method. The random dynamic characteristics of the resonator are then solved by implementing the left and right eigenvectors and the block Lanczos algorithm, and the random temperature field and structural random dynamic stress are also tackled. Afterwards, the overall structural reliability is investigated with a comprehensive consideration of the strength failure and frequency resonance failure, in which the Copula function is used for describing the dynamic correlation between two failure modes. Finally, the feasibility and rationality of the method put forward are demonstrated via a practically motivated example.

Thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction

Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction are investigated analytically and numerically. The corresponding dispersion relation is a sixth-order algebraic equation, governed by six non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter, the ratio between extensional and torsional moduli, the Fourier number, and the dimensionless thermal relaxation. The behavior of the solutions is discussed from two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxation on the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wave celerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered. However, with large wavenumbers, the solutions behave differently depending on the thermal relaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from the classical result of the speed of second sound.

Modified Green–Lindsay model on the reflection and propagation of thermoelastic plane waves at an isothermal stress-free surface

The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al. (Meccanica 53:2543–2554, 2018). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear-type (SV-type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios of the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds and the amplitude ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models.

Dynamic evolution of damage by microcracking with heat dissipation

A new thermo-mechanical damage model is constructed in the present contribution using a two-scale approach. The model is deduced from microstructures with microcracks evolving dynamically in a nominally brittle material and for which the fracture energy dissipated at the moving tips is converted to heat. The use of an homogenization method based on asymptotic developments leads to a damage evolution law coupled with the macroscopic thermoelasticity system. The obtained model accounts for inertial effects, thermo-elastic coupling and heat dissipation effects due to damage propagation. The local effective response of the model is analyzed with special emphasis on thermal evolutions. Strain-rate and microstructural size effects are illustrated. Cooling and heating regimes associated to damage initiation and propagation are identified and analyzed for different values of the model parameters. Results of numerical simulations for a compact compression specimen test are presented and compared with the experimental data for temperature field measurements during rapid failure of PMMA samples. Good agreement is found between the model predictions and the measured thermal evolution.