Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory

Abstract

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

Sound Transmission Loss of a Honeycomb Sandwich Cylindrical Shell with Functionally Graded Porous Layers

“…Also, the transverse deflection of the structure is expressed with W. Furthermore, the rotation angles of the middle plane along θ and x directions are signified by φ θ and φ x , respectively. The displacement and rotation terms are stated as [67,68] U, W,…”

On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams

“…Crystals 2021, 11, 1206 2 of 20 theories were successfully applied to develop size-dependent structure models for very small scales. For example, based on nonlocal theories, a number of MEE/MEE-FGM beam and plate models have been developed to capture non-local size effects [29][30][31][32], in which a non-local medium, including long-range material interactions, is adopted. Lim et al [33] proposed a non-local strain gradient theory to include both non-local and strain gradient effects, and the bending, buckling, and free variation problems of FGM beams have been solved [34,35].…”

Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties

“…where f(x, t) and u(x, t) stand for the variation of the electric and magnetic potentials across the x-direction, respectively; f 0 and u 0 denote the initial external electric and magnetic potentials applied to the MEE nanobeam, respectively, and x = p/h. The nonzero electric field and magnetic field components (E x , E z , H x , H z ) can be separately calculated as (Kiani et al, 2017)…”

“…Moura and Erturk (2018) studied the electro-mechanical coupling response of bimorph cantilevers by considering the piezoelectric, flexoelectric, and small-scale effects. Kiani et al (2017) analyzed the free vibration behavior of MEE nanoplates on the basis of the nonlocal third-order shear deformation theory. Similarly, the vibration characteristics of MEE nanobeams, nanoshells, and nanoplates were discussed by Ke et al (2014bKe et al ( , 2014c and Ke and Wang (2014) with the aid of the nonlocal theory.…”