This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

这项工作旨在基于鲁棒的有限梁单元对具有逐渐变化的机械性能的多孔梁的自由振动行为进行分析。控制方程是使用考虑高阶位移分布的混合变分公式开发的。引入了新的横向剪应变抛物线分布，并满足梁上下表面剪应力为零的条件。孔隙度可以均匀和不均匀地分布到光束中。根据修正的幂函数，材料特性沿 FGM 多孔梁的厚度方向变化。所呈现的结果显示了梯度指数、孔隙率系数和形式、边界条件和几何参数对 FGM 梁振动的影响。