Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

Abstract

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Thermoelastic vibrations in initially stressed rotating microbeams caused by laser irradiation

“…Since 𝛿𝑤 is arbitrary in the range 0 ≤ 𝑥 ≤ 𝐿 and using the integration by parts, the following the motion equation may be obtained [28,32]…”

“…Since $$\delta w$$ is arbitrary in the range $$0 \le x \le L$$ and using the integration by parts, the following the motion equation may be obtained [28, 32] $$\begin{equation} \frac{{{\partial ^2}M}}{{\partial {x^2}}} = \rho A\frac{{{\partial ^2}w}}{{\partial {t^2}}} + \frac{\partial }{{\partial x}}\left[ {\left( {{\sigma _0} - R} \right)\frac{{\partial w}}{{\partial x}}} \right] \end{equation}$$…”

“…Due to the cooling process, temperature difference, shot fixation, cold working, gravitational patterns, external differential power, and so on the initial stresses accumulate in the materials due to various causes. The planet is also exposed to high initial stresses [28]. In this field, researchers use this to analyze and investigate, in addition to stress waves, the effect of certain stresses on the propagation of mechanical waves.…”

Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories

“…So far, the generalized thermoelastic theories have been used to study the dynamic response of microbeam. 59,60 For thermoviscoelastic interactions, Abouelregal and Ahmad 61 formulated a generalized thermoviscoelastic theory based on the thermal wave model and the Kelvin-Voigt viscoelastic model and they analyzed the transient response of a rotating viscoelastic microbeam subjected to a laser pulse heating.…”

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

“…Some interested investigations of TED using MCST can also be found in Refs. Abouelregal (2020); Abouelregal and Marin (2020); Attar et al (2021); Bhattacharya and Das (2019); Kumar (2016); Kumar and Mukhopadhyay (2021); Ebrahimi and Barati (2018); Reddy et al (2016);and Shafiei et al (2017). Kong et al (2009) studied the dynamic and static behavior of microbeams using strain gradient elasticity theory.…”