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.

本研究通过研究由二维功能梯度（2D-FG）多孔材料作为顶部和底部面板以及混合蜂窝结构组成的三层梁的振动行为，提出了一种设计夹层纳米梁的新颖方法（ HCS）作为核心层。 HCS 是一种独特的配置，由两个具有不同晶胞角度的独立部分组成，提供从负到正的各种泊松比。假设面板采用铝和氧化铝，分别为金属和陶瓷。此外，铝被用作中间层蜂窝结构的基材。结合了基于埃林根非局部理论的弹性理论来解释小尺度的影响。采用修正剪切变形理论 (PSDBT) 来推导基于能量法的运动方程。然后用伽辽金法求解。已经进行了实现夹层 HCS 纳米梁单位固有频率的可能性。它将通过改变具有不同角度的蜂窝结构核心层的部分的长度来提供。通过改变单元的角度，可以将核心的泊松比从负值调整为正值。另一个重大成就是可以在不同形状模式下设计具有相同固有频率的夹层梁。通过分析厚度和长度方向上的材料分级指数、混合芯材的孔角、非局部参数、孔隙率和长细比（L/h）等各种参数的影响，该研究为设计提供了新的见解以及具有混合细胞结构的夹心纳米梁的潜在应用。