An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams

Abstract

This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electromagnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electromagnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.

Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates

“…The electric potential and magnetic potential distributions across the thickness are approximated via a combination of a cosine and linear variation to satisfy Maxwell's equation in the quasi-static approximation as follows [32,33]:…”

“…In another work, Li et al [31] researched vibration and buckling behavior of MEE nanosize plates based on nonlocal elasticity. In the case of smart sizedependent FGM structures, Ebrahimi and Barati [32][33][34][35] investigated size-dependent buckling and vibration analysis of functionally graded piezo-magnetic nanobeams. Most recently, Ebrahimi and Barati [36] explored temperature distribution effects on buckling behavior of smart FG nanosize plates based on nonlocal four-variable refined plate theory.…”

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

“…The macro-behaviors of composite structures were derived in the MEE-coupled fields (Chen et al, 2014; Jin and Aboudi, 2015; Wu et al, 2018). Ebrahimi and Barati (2016) reported an exact solution to the bucking performances of functionally graded MEE nanobeams. Analysis with Hamilton’s rule and the nonlocal elasticity rule indicated the internal frequency of size-variable MEE nanoplates was associated with the outside magneto-electric potentials (Farajpour et al, 2016).…”

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

“…(2016) examined size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept. Vibration and buckling analysis of smart piezoelectrically actuated FG nanobeams subjected to magneto-electrical field was performed by Ebrahimi and Barati (2016b–d). Şimşek (2016) explored nonlinear vibration behavior of FG nanobeams, employing nonlocal strain gradient theory presenting a Hamiltonian solution, and analysis of mechanical behavior of FGM nanostructures based on new higher order theories has been performed by several researchers (Al-Basyouni et al., 2015; Belkorissat et al., 2015; Bouafia et al., 2017; Bounouara et al., 2016; Larbi Chaht et al., 2015; Zemri et al., 2015).…”