Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model

Kumar, Harendra; Mukhopadhyay, Santwana

doi:10.1016/j.ijheatmasstransfer.2019.118997

Cited by 59 publications

(5 citation statements)

References 44 publications

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“…𝜒 23 (1) 𝑥 3 𝜒 31 (3) 𝑥 3 3 + 𝑥 3 𝜒 31 (1) + 𝜒 31 (0) 𝜒 32 (3) 𝑥 3 3 + 𝑥 3 𝜒 32 (1) + 𝜒 32 (0) 𝜒 33 (2) 𝑥 3 2 + 𝜒 33…”

Section: Governing Equationsunclassified

“…where V (1) = vector of dimensional values, 𝑆 = 𝑆 𝑐𝑙 +𝑆 𝑛𝑐𝑙 = the 'classical' and 'nonclassical' parts. 𝑀 = 𝑀 𝑐𝑙 as the kinetic energy does not include any sizedependent parameters.…”

Section: Natural Frequencies and Free Vibrationmentioning

confidence: 99%

“…Such micro-and nano-objects can be a part of high precision measuring devices. For example, they can be sensing elements that act as very high frequency resonators [1]. Yang, et al [2] describes the resonator for inertial mass sensing with proved 7 zg resolution.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

Barulina

Kondratov

Galkina

et al. 2022

J. Math. Fund. Sci.

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In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton’s principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1.

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“…𝜒 23 (1) 𝑥 3 𝜒 31 (3) 𝑥 3 3 + 𝑥 3 𝜒 31 (1) + 𝜒 31 (0) 𝜒 32 (3) 𝑥 3 3 + 𝑥 3 𝜒 32 (1) + 𝜒 32 (0) 𝜒 33 (2) 𝑥 3 2 + 𝜒 33…”

Section: Governing Equationsunclassified

Section: Natural Frequencies and Free Vibrationmentioning

confidence: 99%

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Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

Barulina

Kondratov

Galkina

et al. 2022

J. Math. Fund. Sci.

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show abstract

“…Each term of (2) relates to an energy loss mechanism. Q air denotes the air or viscous energy loss which occurs due to the compressive force of the peripheral medium (e.g., air) onto the surface of the resonator [8,9], Q TED is the thermo-elastic damping that is caused by the induced temperature gradient by the mechanical vibration of the resonator [10][11][12], and Q sur f ace is the surface loss that is caused by the existence of a thin layer of contaminations and defects on the surface of the resonator [13]. In addition, Akhiezer damping [14] is another source of energy loss in resonators comprehensively studied by [15].…”

Section: Introductionmentioning

confidence: 99%

Anchor Loss Reduction in Micro-Electro Mechanical Systems Flexural Beam Resonators Using Trench Hole Array Reflectors

Kazemi,

Nabavi,

Gratuze

et al. 2023

Micromachines

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The quality factor of microelectromechanical resonators is a crucial performance metric and has thus been the subject of numerous studies aimed at maximizing its value by minimizing the anchor loss. This work presents a study on the effect of elastic wave reflectors on the quality factor of MEMS clamped–clamped flexural beam resonators. The elastic wave reflectors are a series of holes created by trenches in the silicon substrate of the resonators. In this regard, four different shapes of arrayed holes are considered, i.e., two sizes of squares and two half circles with different directions are positioned in proximity to the anchors. The impact of these shapes on the quality factor is examined through both numerical simulations and experimental analysis. A 2D in-plane wave propagation model with a low-reflecting fixed boundary condition was used in the numerical simulation to predict the behavior, and the MEMS resonator prototypes were fabricated using a commercially available micro-fabrication process to validate the findings. Notably, the research identifies that half-circle-shaped holes with their curved sides facing the anchors yield the most promising results. With these reflectors, the quality factor of the resonator is increased by a factor of 1.70× in air or 1.72× in vacuum.

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“…Considering plane stress and plane strain conditions, Rezazadeh et al (2012) derived analytical expression of TED in gold and nickel microbeam resonators using MCST. 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.…”

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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Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model

Cited by 59 publications

References 44 publications

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

Anchor Loss Reduction in Micro-Electro Mechanical Systems Flexural Beam Resonators Using Trench Hole Array Reflectors

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

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