Small-scale analysis of plates with thermoelastic damping based on the modified couple stress theory and the dual-phase-lag heat conduction model

Borjalilou, Vahid; Asghari, Mohsen

doi:10.1007/s00707-018-2197-0

Cited by 47 publications

(7 citation statements)

References 58 publications

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“…According to the DPL model, which has a unified form of heat conduction, the heat flux vector bold-italicq and gradient of temperature increment ∇θ are related to each other for isotropic materials by the following hyperbolic constitutive relation (Borjalilou and Asghari, 2018; Tzou, 2014)where k is the thermal conductivity of material. Parameter τq represents the phase lag of heat flux, which enables the model to take into account small-scale effect in time.…”

Section: Theoretical Preliminariesmentioning

confidence: 99%

“…In a similar work to Zhang et al (2016) and Yu et al (2017) employed the nonlocal elasticity theory instead of MCST to derive a size-dependent relation for estimating TED in microbeam resonators. Using the MCST and DPL heat conduction model, Borjalilou and Asghari (2018) obtained an exact formula including small-scale effects for TED in thin microplates. Rashahmadi and Meguid (2019) developed a model based on the nonlocal theory to determine the amount of TED in orthotropic graphene nanosheets.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Theoretical Preliminariesmentioning

confidence: 99%

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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“…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%

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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“…Malikan et al (2017) analyzed the electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory [143]. Borjalilou et al (2018) explored the small-scale effects on the thermoelastic damping in microplates applying strain gradient theory and the impacts of certain parameters on thermoelastic damping is analysed [144]. Thai (2018) et al presented a non-classical model for bending, free vibration and buckling analyses of functionally graded (FG) isotropic and sandwich microplates based on the modified couple stress theory MCST and the refined higher order shear deformation theory [145].…”

Section: Introductionmentioning

confidence: 99%

Impacts of Length Scale Parameter on Material Dependent Thermoelastic Damping in Micro/nanoplates Applying Modified Coupled Stress Theory

Resmi

BABU

BAIJU

2022

mech

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Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and need tobe alleviated in resonators inorder to enhance its performance parameters by improving its thermoelastic dampinglimited qualityfactor, QTED. The maximum energy dissipation is also interrelated with critical length (???????? ) of theplates and by optimizing the dimensions the peaking of energy dissipation can be diminished. As the size of thedevices is scaled down, classical continuum theories are not able to explain the size effect related mechanicalbehavior at micron or submicron levels and as a result non-classical continuum theories are pioneered with theinception of internal length scale parameters. In this paper, analysis of isotropic rectangular micro-plates based onKirchhoff model applying Modified Coupled Stress Theory is used toanalyzethe size-dependent thermoelasticdamping and its impact on quality factor and critical dimensions.Hamilton principle is adapted to derive thegoverning equations of motion and the coupled heat conduction equation is employed to formulate the thermoelasticdamping limited quality factor of the plates. Five different structural materials (PolySi, Diamond,Si, GaAs andSiC)are used for optimizing QTED which depends on the materialperformance index parameters. ThermoelasticDamping Index [TDI] and thermal diffusion length, lT. According to this work, the maximum QTED is attained forPolySi with the lowest TDI and Lcmax is obtained for SiC which is having the lowest lT. The impact of lengthscaleparameters (l), vibration modes, boundary conditions (Clamped–Clamped and Simply Supported), and operatingtemperatures on QTED and Lcare also investigated. It is concluded that QTED is further maximized by selecting lowtemperatures and higher internal length scale parameters (l).The prior knowledge of QTED and Lchelp the designers tocome out with high performance low loss resonators.

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Small-scale analysis of plates with thermoelastic damping based on the modified couple stress theory and the dual-phase-lag heat conduction model

Cited by 47 publications

References 58 publications

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

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

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

Impacts of Length Scale Parameter on Material Dependent Thermoelastic Damping in Micro/nanoplates Applying Modified Coupled Stress Theory

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