Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model

Borjalilou, Vahid; Asghari, Mohsen; Bagheri, Emadoddin

doi:10.1080/01495739.2019.1590168

Cited by 68 publications

(12 citation statements)

References 44 publications

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“…To capture long-range effects, Eringen [6] considered that the nonlocal strain of points under translational motion is the same with that of the classical theory, but the stress at a point is relevant to the strain in a region near that point. In recent years, researchers' attention has been devoted to survey static [8][9][10][11][12], vibration [13,14], buckling and postbuckling [15][16][17], dynamic [18][19][20][21] and thermomechanical [22][23][24][25][26] behavior of micro-and nanostructures according to the nonclassical continuum theories such as the nonlocal, modified couples stress and modified strain gradient theories.…”

Section: Small-scale Effectmentioning

confidence: 99%

“…In this section, an exact solution for the free vibration behavior of CNTRC beams is developed. First, substituting for stress resultants from (19), (21) and (22) into (18) results in the nonlocal motion equations of CNTRC beams in terms of displacement components as follows: in which, is the natural frequency. Next, substituting Eq.…”

Section: Free Vibration Behaviormentioning

confidence: 99%

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Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

2019

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This paper investigates the bending, buckling and free vibration behaviors of functionally graded carbon nanotubereinforced composite (FG-CNTRC) nanobeams by considering small-scale effect. The governing equations of motion of a Timoshenko beam under a general loading are derived utilizing the nonlocal elasticity theory. The equations governing bending and stretching behavior of CNTRC nanobeams are uncoupled to a fifth-order ordinary differential equation with respect to the rotation of cross-section for the static cases of bending and buckling. This uncoupling makes it possible to develop exact solutions for transverse deflection and buckling load of CNTRC nanobeams. Using differential operator method, the decoupled sixth-order differential equations in terms of the kinematic variables are obtained for vibration analysis. By setting the coefficients matrix in the corresponding system of homogenous algebraic equations to zero, an algebraic frequency equation is derived. Finally, based on the presented closed-form solutions, parametric studies are carried out to assess the effects of CNT distribution, nonlocal parameter and type of boundary conditions on the deflection, buckling and natural frequency of CNTRC nanobeams. Findings show that nonlocal effect on the mechanical behavior of nanobeams is strongly dependent on boundary conditions and loadings. It is seen that cantilever nanobeams become harder by taking into account nonlocal effect, contrary to clamped and simply supported nanobeams. In addition, the influence of CNT distribution on the mechanical behavior of cantilever beams is more significant than that of simply supported and clamped beams.

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Section: Small-scale Effectmentioning

confidence: 99%

Section: Free Vibration Behaviormentioning

confidence: 99%

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

2019

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“…Kumar and Mukhopadhyay (2020b) illustrated TED in microplate resonators using MCST and thermoelasticity theory with three-phase-lagging effects. Borjalilou et al (2019) used dual-phase-lag heat conduction equation and MCST to analyze TED in microbeams/plates. Some interested investigations of TED using MCST can also be found in Refs.…”

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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“…To solve the coupled thermoelastic equations, they used the semi-analytical Galerkin method. Borjalilou et al (2019) employed the MCST and DPL heat conduction models to investigate the small-scale effect on the TED in Euler–Bernoulli microbeams. With the aid of a Galerkin-based reduced order model, an analytical relation for computing TED in electrically actuated microbeams has been presented in the work of Borjalilou and Asghari (2019).…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect

Borjalilou

Asghari

Taati

2020

Journal of Vibration and Control

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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 small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To clarify the influence of nonlocality and dual-phase-lagging on the amount of thermoelastic damping, numerical results are compared with the ones predicted in the framework of classical continuum and heat conduction theories. Findings reveal that the size effect on both the continuum mechanics and heat conduction modeling of nanobeams is not negligible. A number of parametric studies are also conducted to indicate the effect of beam dimensions, boundary conditions and type of material on the value of thermoelastic damping.

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Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model

Cited by 68 publications

References 44 publications

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

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

Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect

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