An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory

Kakhki, Ehsan Kazemnia; Hosseini, Seyed Mahmoud; Tahani, Masoud

doi:10.1016/j.apm.2015.10.019

Cited by 65 publications

(7 citation statements)

References 30 publications

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“…The Lord-Shulman (L-S) model presents thermoelasticity with one relaxation time. L-S model gives heat conduction relation as [50][51][52][53][54][55]:…”

Section: Let Us Consider Small Flexural Displacements For the Microbe...mentioning

confidence: 99%

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

Malikan

Eremeyev

2022

Arch Appl Mech

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We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.

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“…The Lord-Shulman (L-S) model presents thermoelasticity with one relaxation time. L-S model gives heat conduction relation as [50][51][52][53][54][55]:…”

Section: Let Us Consider Small Flexural Displacements For the Microbe...mentioning

confidence: 99%

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

Malikan

Eremeyev

2022

Arch Appl Mech

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“…In an equilibrium state, the nanobeam has no damping, unstressed, unstrained and the reference temperature is T 0 everywhere. 6…”

Section: Problem Formulationmentioning

confidence: 99%

“…Its work also reveals that the deflection vibrates in a simulated state mode when the thermal moment springs and vibrates in the same mode as the deflection at first. In the form of the updated theory of couple tension, Kazemnia Kakhki et al 6 studied TED and microbeam resonator dynamical behaviour using the theory of thermoelasticity. For the solution of thermoelastic variations and the representation of the beam deflection and thermoelectric moment, the Laplace Transformation technology was adopted.…”

Section: Introductionmentioning

confidence: 99%

The vibration of thermoelastic silicon nitride Nanobeam based on green-naghdi theorem type-II subjected to mechanical damage and ramp-type heat

Youssef

Alharthi

Kurdi

2021

The Journal of Strain Analysis for Engineering Design

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In this work, an analysis for thermoelastic homogeneous isotropic nanobeams under damage mechanics consideration was built. Under easily supported boundary conditions with fixed side ratios, the Green-Naghdi model type-II, an extended thermoelasticity theory model, has been utilized. For the governing differential equations, the Laplace transforms technique was used on the time variable. The answers were found in the domain of the Laplace transform. Tzou’s approximation approach based on an iteration formula was used to calculate the Laplace transform inversions numerically. The numerical findings for a rectangular silicon nitride thermoelastic nanobeam have been obtained and validated. As a case study, we assumed that the beam is thermally loaded with ramp-type heat and that its two edges are simply supported. Figures representing different scenarios have been used to display the numerical results. Mechanical damage value, ramp-time heat parameter and beam thickness are all reported to have a substantial influence on all of the examined functions.

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“…On the other hand, the upper limitation of the quality factor is dominated by thermoelastic damping (TED) (Lifshitz and Roukes, 2000). The TED mechanism (Kim and Kim, 2021; Kakhki et al, 2016) is an intrinsic energy dissipation process that may be illustrated as when a resonator is subjected to harmonic excitation, an irreversible heat flow is generated due to the temperature difference between the stretched and compressed regions during the oscillation. As a result, some mechanical energy is transformed to thermal energy.…”

Section: Introductionmentioning

confidence: 99%

“…Zhong et al (2014) investigated size-dependent TED in microplate resonators utilizing MCST and demonstrated that the size effect has a significant impact on TED when the plate thickness is nearer to material length-scale parameter. Based on MCST, Kakhki et al (2016) analyzed TED in microbeams using the generalized theory of thermoelasticity. Considering plane stress and plane strain conditions, Rezazadeh et al (2012) derived analytical expression of TED in gold and nickel microbeam resonators using MCST.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent thermoelastic damping analysis in nanobeam resonators based on Eringen’s nonlocal elasticity and modified couple stress theories

Kumar

Mukhopadhyay

2022

Journal of Vibration and Control

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Thermoelastic damping has emerged as a critical issue in the modeling and design of micro and nanomechanical systems. Therefore, an extensive research interest is being devoted towards the reduction in thermoelastic damping for micro and nanomechanical systems. The present study intends to examine thermoelastic damping in nanobeam resonators using the modified couple stress theory and Eringen’s nonlocal elasticity theory, thus so-called modified nonlocal couple stress theory within the context of the recently proposed Moore–Gibson–Thompson thermoelasticity theory. In order to observe size effects, the size-dependent coupled thermoelastic equations are derived by combining modified couple stress theory and nonlocal elasticity theory in the frame of Moore–Gibson–Thompson thermoelasticity. The coupled governing equations for thermoelastic damping of nanobeam resonators are solved analytically in terms of the inverse quality factor. The size-dependent thermoelastic damping of nanobeams is presented graphically with the help of numerical results predicted by modified nonlocal couple stress theory. The results obtained under the combined effects of modified couple stress theory and nonlocal theory in the present context are further compared to those of the classical, modified couple stress, and nonlocal elasticity theories as special cases of the modified nonlocal couple stress theory. It is observed that thermoelastic damping weakens at the submicron scale under Eringen’s nonlocal elasticity theory, whereas it becomes greater at the submicron scale under modified couple stress theory. However, at the submicron scale, the modeling of nanobeam resonators using modified nonlocal couple stress theory reveals a smaller amount of thermoelastic damping than modified couple stress, nonlocal, and classical theories. In addition, as compared to the Green–Naghdi thermoelasticity theory of type III (GN-III), the Moore–Gibson–Thompson model predicts a higher thermoelastic damping value, while agreeing with the results predicted by the Lord–Shulman (LS) model under modified nonlocal couple stress theory. Some important points highlighted here are believed to be useful in the design of mechanical resonators at micron and submicron scales.

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An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory

Cited by 65 publications

References 30 publications

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

The vibration of thermoelastic silicon nitride Nanobeam based on green-naghdi theorem type-II subjected to mechanical damage and ramp-type heat

Size-dependent thermoelastic damping analysis in nanobeam resonators based on Eringen’s nonlocal elasticity and modified couple stress theories

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