Thermal-mechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory

Abstract

This paper presents thermal-mechanical-electrical buckling analysis of micro-beams that are made of functionally graded materials(FGMs) with temperature-dependent thermo-elastic properties. The material properties of the micro-beam are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the principle of the minimum total potential energy, von Kármán geometric nonlinearity theory, and modified couple stress theory is employed to consider the size effect. A differential quadrature (DQ) method combined with an iteration process is used to predict the critical buckling external axial force and buckling temperature increment. The effects of the volume fraction profile parameter, dimensionless length scale parameter, initial gap ratio, ground electrode shape parameter, the applied voltage, slenderness ratio and the axial residual stress on the thermal-mechanical-electrical buckling behavior are evaluated in detail through parametric studies.

Free vibration of microscale frameworks using modified couple stress and a combination of Rayleigh–Love and Timoshenko theories

“…Using the MCST, several studies have accounted for size-effect in the analyses of miniaturised structures. On the one hand, there are investigations with objectives associated with the analyses of standalone micro-structures, for instance, microbeams with mechanical loads (Dehrouyeh-Semnani and Nikkhah-Bahrami, 2015; Park and Gao, 2006; Şimşek, 2010), microbeams under electromechanical loads (Abdi et al, 2011; Attia and Emam, 2018; Fakhrabadi and Yang, 2015), thermo-electro-mechanical loading (Jia et al, 2018), geometrically nonlinear behaviour of microbeams (Dai et al, 2015; Ghayesh and Farajpour, 2018; Sedighi et al, 2014), piezoelectric microbeams (Ansari et al, 2014; Tan and Chen, 2019), composite laminated beams (Chen and Li, 2013), microplates (Farokhi and Ghayesh, 2015; Kim et al, 2019; Zandekarimi et al, 2018) and microshells (Jouneghani et al, 2018; Zeighampour and Beni, 2015). On the other hand, the MCST has also been applied to integrated microscale systems (Fard et al, 2018; Mustapha and Ruan, 2015).…”

Chaotic dynamics of size‐dependent curvilinear Euler–Bernoulli beam resonators (MEMS) in a stationary thermal field

“…Here and further, the temperature field is given in dimensional form for the case of zinc oxide (ZnO) and in the considered temperature interval of the beam the material characteristics remain unchanged. In order to carry out transition into dimensional temperature values we have used the following fixed parameters: = 2.1 × 10 5 mPa, = 6.5 × 10 −6 1/grad and = Δ + 0 , 0 = 22 • , where Δ denotes increment of the temperature ( , ) defined via the heat transfer PDE (7) subjected to (8).…”

“…Jia et al. [8] analyzed functionally graded material with temperature‐dependent thermo‐elastic properties of nanobeams with regard to their buckling effects. The minimum total potential energy principle yielded the governing equations with an account of von Kármán geometric nonlinearity and modified couple stress theory.…”

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

“…Composite beams in this context are analysed in [15][16][17][18][19]. These analyses tend to account for other phenomena and become rather complex, like in the thermo-electro-mechanical analysis of functionally graded size dependent beams [20]. Non-probabilistic uncertainty modelling for vibration and buckling of the FG nanobeams in nonisothermal conditions is considered in [21].…”