Abstract
This study investigates the free vibration behaviour of piezoelectric multi-layered functionally graded nanocomposite beams reinforced with graphene platelets (GPLs) under combined thermal and electrical fields. Different GPLs distribution patterns are considered to enhance the mechanical performance of the material. The effective properties are estimated using the rule of mixtures and the modified Halpin–Tsai model. The equations of motion are derived within the quasi-3D beam theory, accounting for shear deformation and stretching effects. For the numerical solution, the Differential Quadrature Finite Element Method (DQ-FEM) is employed, offering high accuracy and computational efficiency. Results reveal that increasing temperature and applied electric potential reduce the structural stiffness and natural frequencies, with the effect becoming more pronounced at higher GPL contents and piezoelectric coefficients. A comprehensive parametric study demonstrates the influence of GPL distribution, volume fraction, beam geometry, number of layers, and boundary conditions on the vibration response, highlighting the strong coupling between thermal, electrical, and mechanical fields in such smart nanocomposite structures.