Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity

This study models and examines the thermal vibration and buckling behaviours of a porous nanoplate made of functional grading of barium-titanate and cobalt-ferrite. The porosity in the nanoplate is modelled with uniform and symmetrical porosity distribution functions. In the constitutive equation of the nanoplate, the strains are assumed to originate from classical mechanics, thermal expansion, electroelastic and magnetostrictive properties, nonlocal elasticity, and strain gradient elasticity. The motion equations of magneto-electro-elastic (MEE) nanoplate is obtained by Hamilton's principle. The study investigated the effects of thermal stresses, magneto-electro-elastic coupling, externally applied electric and magnetic field potential, nonlocal properties (nonlocal and material size parameters), and porosity volume fraction and function of porosity variation across thickness in free vibration and buckling behaviour of the nanoplate. According to the analysis results, the dimensionless frequencies decrease as the barium-titanate ratio in the nanoplate increases, and the frequencies increase as the cobalt-ferrite ratio increases, depending on the material grading index. While temperature increased and porosity ratio decreased dimensionless frequencies, external magnetic potential increased dimensionless frequencies. On the other hand, the application of electric potential causes a slight increase in dimensionless frequencies compared to the effect of magnetic potential.