A general formulation of quality factor for composite micro/nano beams in the air environment based on the nonlocal elasticity theory

Nazemizadeh, Mostafa; Bakhtiari-Nejad, Firooz

doi:10.1016/j.compstruct.2015.05.070

Cited by 12 publications

(6 citation statements)

References 44 publications

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“…Khanchehgardan et al (2013) studied TED in Euler–Bernoulli nanobeam resonators based on nonlocal elasticity theory. A general formulation of the quality factor considering composite micro/nanobeams in the air environment under nonlocal theory has been derived by Nazemzadeh and Bakhtiari-Nejad (2015). Lu et al (2006) established a nonlocal Euler–Bernoulli beam model utilizing nonlocal elasticity theory in order to analyze the dynamic properties of nanobeams.…”

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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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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“…Nazemizadeh et al. [9] employed the nonlocal elasticity theory to investigate size‐dependent vibration of micro/nano composite beams having arbitrary laminated layers and longitudinal discontinuities. Also, they [10] investigated nonlinear vibration of piezoelectric laminated nanobeams at higher modes based on nonlocal piezoelectric theory.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, many researches have demonstrated size-dependent behaviour of such structures and various size-dependent theories have been presented to predict the size effects on micro/nano structures. Nazemizadeh et al [9] employed the nonlocal elasticity theory to investigate sizedependent vibration of micro/nano composite beams having arbitrary laminated layers and longitudinal discontinuities. Also, they [10] investigated nonlinear vibration of piezoelectric laminated nanobeams at higher modes based on nonlocal piezoelectric theory.…”

Section: Introductionmentioning

confidence: 99%

Size‐dependent static bending of anisotropic rectangular nanoplates with cubic crystal structures

Assadi

Najaf

Nazemizadeh

2021

Micro & Nano Letters

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“…Tan et al (2016Tan et al ( , 2018 demonstrated approaches for the free vibrations of cracked and non-cracked non-uniform beams. Nazemizadeh and Bakhtiari-Nejad (2015) investigated the quality factor of composite micro-/nano-beams using the non-local Euler-Bernoulli beam theory. Similarly, Wei (2001bWei ( , 2001cWei ( , 2002a also tested his numerical approach, discrete singular convolution (DSC), on uniform bars and beams in his early studies.…”

Section: Introductionmentioning

confidence: 99%

Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

Seçgin

Kara

Ferguson

2021

Journal of Vibration and Control

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This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.

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A general formulation of quality factor for composite micro/nano beams in the air environment based on the nonlocal elasticity theory

Cited by 12 publications

References 44 publications

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

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

Size‐dependent static bending of anisotropic rectangular nanoplates with cubic crystal structures

Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

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