Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.

基于一阶剪切变形理论，研究了功能梯度框架结构的振动响应和带隙特性。功能梯度材料棒的材料特性根据幂定律在厚度方向上连续变化。详细推导了整体坐标系统中周期性功能梯度材料框架结构的光谱刚度矩阵。因此，可以通过使用谱元法来计算和分析功能梯度材料框架结构的振动带隙特性。通过有限元方法验证了功能梯度材料框架结构动力响应的计算精度。结果表明，与同质框架相比，功能渐变框架结构在低频和中频范围内可实现更宽的带隙。此外，通过设计功能梯度材料杆的梯度指数，可以有效地调节功能梯度材料框架结构的带隙的频率窗口和范围，这为抑制框架结构的振动提供了新思路。