This study investigates the vibrational behavior of a variable thickness sandwich beam resting on a three-parameter elastic foundation. The beam's thickness decreases gradually along its length, and its core is made from functionally graded porous materials. The facesheets are reinforced with graphene nanoplatelets, and the stress transformations at specific angles are necessary to compute the equivalent properties. Hamilton's principle and a variational approach are used to derive the governing motion equations and boundary conditions. The generalized differential quadrature method is employed to solve these equations under various boundary conditions, analyzing the effects of parameters such as geometry, porosity coefficient, distribution porosity, graphene dispersion patterns, and the angle of transformation on the natural frequencies. The introduction highlights the significance of variable thickness beams in various applications, including aircraft wings, mechanical systems, bridges, composite materials, and seismology. It also discusses the advantages of sandwich structures, particularly their strength-to-weight ratio and stiffness, and the role of core materials in providing structural integrity. The study references previous research on porous and nanocomposite materials, emphasizing the enhanced properties of graphene nanoplatelets in nanocomposites.This study investigates the vibrational behavior of a variable thickness sandwich beam resting on a three-parameter elastic foundation. The beam's thickness decreases gradually along its length, and its core is made from functionally graded porous materials. The facesheets are reinforced with graphene nanoplatelets, and the stress transformations at specific angles are necessary to compute the equivalent properties. Hamilton's principle and a variational approach are used to derive the governing motion equations and boundary conditions. The generalized differential quadrature method is employed to solve these equations under various boundary conditions, analyzing the effects of parameters such as geometry, porosity coefficient, distribution porosity, graphene dispersion patterns, and the angle of transformation on the natural frequencies. The introduction highlights the significance of variable thickness beams in various applications, including aircraft wings, mechanical systems, bridges, composite materials, and seismology. It also discusses the advantages of sandwich structures, particularly their strength-to-weight ratio and stiffness, and the role of core materials in providing structural integrity. The study references previous research on porous and nanocomposite materials, emphasizing the enhanced properties of graphene nanoplatelets in nanocomposites.