A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment

Abstract

A simplified three-unknown shear and normal deformations nonlocal beam theory for thermo-electro-magneto mechanical bending analysis of a nanobeam with a functionally graded material core and two functionally piezomagnetic layers is studied in this paper. The assumed structure is subjected to mechanical, thermal, electrical, and magnetic loads. An initial applied voltage and magnetic load is considered on the functionally graded piezomagnetic material layers. Eringen’s nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using the principle of virtual displacements. The numerical results including the deflection, electric, and magnetic potential distribution are calculated in terms of important parameters of the problem such as applied electric and magnetic potentials, two parameters of temperature distribution, and nonlocal parameter. The numerical results indicate that increase in applied electric potential increases the deflection unlike the applied magnetic potential that decreases the deflection. Furthermore, it can be concluded that increasing the nonlocal parameter leads to increase in the deflection.

Transient analysis of a three-layer microbeam subjected to electric potential

“…Before presentation of the numerical results, the material properties of core and piezoelectric face-sheets may be presented as ( [8,[18][19][20][21]25]…”

“…By considering the electric potential, we can complete required equations. A two-dimensional electric potential with an applied voltage is employed as following format [18][19][20][21]:…”

“…Arefi and Zenkour [18] employed simplified shear and normal deformations nonlocal theory for bending analysis of FG piezomagnetic sandwich nanobeams. The nanobeam was subjected to thermal, mechanical, electrical, and magnetic loads.…”

On thermomechanics of multilayered beams

“…Sandwich beams operate in many engineering applications. For instance, piezoelectric effects can be involved, so these are also included in the formulation [36][37][38]. A combination of sandwich and functionally graded (FG) materials including thermal effects are also considered and stability issues in the presence of dynamic effects are analyzed in [39,40].…”

Thermoelastic response of nanobeam resonators subjected to exponential decaying time varying load

“…The basic difference between both classical and nonlocal elasticity theories is based on the definition of stress. Eringen's nonlocal theory includes more information about long range forces about atoms and, thus, internal scale length is introduced (Arefi and Zenkour, 2016;Zenkour, 2016a,c;Zenkour and Abouelregal, 2014a,b, 2015.…”