Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams

In this article, the size-dependent and porosity-dependent vibrational behavior of magneto-electro-elastic functionally graded (MEE-FG) nanoscale beams on two-parameter elastic substrate is presented via a third-order shear deformation beam model. Porosity-dependent material coefficients of the nanobeam are compositionally graded throughout the thickness according to a modified power-law model. Incorporation of small size effect is carried out based on Eringen's nonlocal elasticity theory. Through Hamilton's principle, derivation of nonlocal governing equations is performed. After analytically solving these equations, the influences of porosity, elastic foundation, magnetic potential, applied voltage, scale coefficient, material gradation and slenderness ratio on the frequencies of the porous MEE-FG nanobeams are examined.