Analytical and meshless DQM approaches to free vibration analysis of symmetric FGM porous nanobeams with piezoelectric effect

The current study is an first attempt to develop a vibrational-based piezoelectrically actuated smart nanoactuator model based on assumptions of Reddy third-order shear deformation beam model together with nonlocal strain gradient theory. The considered model is a sandwich structure consisting of piezoelectric layers under an external electric field, and symmetric to the midplane functionally graded (FG) porous core. Expressed by displacements equations of motion are derived based on a dynamic version of Hamilton's principle. Eigenvalue problem of free vibration of simply supported nanobeam is solved analytically by using properties of Fourier series, and numerically via meshless Differential Quadrature Method (DQM). The study includes a convergence study for the numerical approach, as well detailed discussion on obtained results involving effects of nonlocal parameters, external mechanical and electrical loads, material gradation coupled with diverse porosity distribution, and influence of external environment on dynamic behavior of the nanostructure. The present paper, in view of included optimization study, may positively affect nanodevices reliability and extend its operation by avoiding resonance phenomenon.