<p>Advanced nanostructures in aerospace and nano-electromechanical systems increasingly require spatially tailored stiffness distributions to withstand multi-directional loading conditions. This study establishes a novel isogeometric analysis (IGA) framework integrating nonlocal strain-gradient theory (NSGT) and sinusoidal shear deformation theory (SSDT) to investigate the geometrically nonlinear free vibration of variable-thickness bidirectionally functionally graded graphene platelet-reinforced composite (BFG-GPLRC) nanoplates with square, annular, and sector-annular geometries. The thickness varies along the in-plane direction (length direction for square nanoplates, radial direction for annular geometries), while GPLs volume fractions exhibit bidirectional gradation along both in-plane and thickness directions. Effective material properties are determined using the modified Halpin–Tsai micromechanical model. The governing equations incorporating both nonlocal softening and strain-gradient hardening mechanisms are discretized using nonuniform rational B-splines (NURBS) basis functions that satisfy the higher-order continuity requirements imposed by NSGT. Following comprehensive validation, extensive parametric studies examine how geometric parameters, material parameters, size-dependent parameters, boundary conditions, and vibration amplitude collectively influence the nonlinear vibration response. Critical findings reveal that nanoplates with thickness decreasing along the radial direction exhibit stronger amplitude-dependent nonlinear behavior and heightened sensitivity to size-dependent effects compared to those with thickness increasing along the radial direction.</p>