This study presents a novel approach to the design of sandwich nanobeams by investigating the vibrational behavior of a three-layer beam comprised of bi-dimensional functionally graded (2D-FG) porous material as the top and bottom face sheets and a hybrid cellular structure (HCS) as the core layer. The HCS is a unique configuration consisting of two separate parts with different unit cell angles, offering a wide range of Poisson ratios from negative to positive. Aluminum and alumina are assumed for face sheets as metal and ceramic, respectively. Also, aluminum is used as the base material for the cellular structure in the middle layer. An elasticity theory based on Eringen’s nonlocal theory is incorporated to account for the effects at small scales. Modified shear deformation theory (PSDBT) is implemented to derive the equations of motion based on the energy method. Afterward, they are solved by the Galerkin method. The possibility of achieving a unit natural frequency of sandwich HCS nanobeam has been conducted. It will be provided by changing the length of parts of the cellular structure core layer with distinct angles. Poisson’s ratios of the core can be adjusted from negative values to positive by altering the angle of cells. Another significant achievement is that sandwich beams with the same natural frequencies can be designed under different shape modes. By analyzing the effect of various parameters, such as material graduation indexes in both directions of thickness and length, the cellular angle of hybrid core, nonlocal parameter, porosity, and slenderness ratios (L/h), the study offers new insights into the design and potential applications of sandwich nanobeams with hybrid cellular structures.
