Large-Deflection Effect on Thermoelastic Dissipation of Microbeam Resonators

Tunvir, K.; Ru, C. Q.; Mioduchowski, A.

doi:10.1080/01495739.2012.720474

Cited by 15 publications

(5 citation statements)

References 31 publications

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“…Figure 6a shows that the values of ω 2 F =0 obtained from Eqs. (96) and (97) practically coincide only for both values of L, i.e. if the Timoshenko model is close to the Bernoulli-Euler model.…”

Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 93%

“…In reference [111] a similar approach has been employed to find approximate value ω 2 F =0 using the Bernoulli hypothesis ∂w 0 /∂ x = −ψ 0 . If we neglect Poisson's effect, (96) yields…”

Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 99%

“…if the Timoshenko model is close to the Bernoulli-Euler model. Therefore, we employ formula (96) to detect the size-dependent frequencies ω 2 F =0 . In the case of the simply supported beam the analysis is simpler.…”

Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 99%

“…The authors of reference [96] studied nonlinear effects under large deflections and under thermoelastic dissipation of the microbeam resonators for adiabatic/isothermic beam surfaces. The models of thermoelasticity and thermoelastic dissipation were formulated for the case of large amplitude vibrations for the Euler-Bernoulli beam without the size-dependent effects.…”

Section: Introductionmentioning

confidence: 99%

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Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

et al. 2019

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The dependence of the quality factor of nonlinear microbeam resonators under thermoelastic damping for Timoshenko beams with regard to geometric nonlinearity has been studied. The constructed mathematical model is based on the modified cou-Russian Federation 634050 ple stress theory which implies prediction of sizedependent effects in microbeam resonators. The Hamilton principle has yielded coupled nonlinear thermoelastic PDEs governing dynamics of the Timoshenko microbeams for both plane stresses and plane deformations. Nonlinear thermoelastic vibrations are studied analytically and numerically and quality factors of the resonators versus geometric and material microbeam properties are estimated. Results are presented for gold microbeams for different ambient temperatures and different beam thicknesses, and they are compared with results yielded by the classical theory of elasticity in linear/nonlinear cases.

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Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 93%

Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 99%

Section: Analytical Solution For the Linear Size-dependent Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

et al. 2019

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“…In stark contrast, nonlinear thermoelastic dissipation has received relatively little attention. The literature is sparse and focuses mainly on the following three types of nonlinearities: (i) geometric nonlinearities due to large deformations, (ii) material nonlinearity due to the temperature dependence of mechanical properties, and (iii) transduction nonlinearities in oscillators caused by electrostatic actuation [ 6 – 15 ]. In this paper, we address a fourth type of nonlinearity whose origins reside at the heart of the thermoelastic coupling that gives rise to dissipation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators

Nourmohammadi¹,

Joshi²,

Vengallatore³

2016

PLoS ONE

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The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.

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Thermoelastic Vibrations of Timoshenko Microbeams (Modified Couple Stress Theory)

Awrejcewicz

Krysko

Zhigalov

et al. 2020

Advanced Structured Materials

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Large-Deflection Effect on Thermoelastic Dissipation of Microbeam Resonators

Cited by 15 publications

References 31 publications

Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators

Thermoelastic Vibrations of Timoshenko Microbeams (Modified Couple Stress Theory)

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