The free vibrational characteristic of PFGM beams near the post-buckling configuration under thermal loads

In recent years, the study of the static and dynamic mechanical behavior of porous functionally graded material (PFGM) structures has attracted much interest. However, most of the existing studies analyze their static or dynamic behaviors independently, and pay little attention to their buckling-vibration coupling mechanical responses under complex loading conditions. Firstly, a linear vibrations mechanical model for PFGM sandwich beams near their post-buckling configuration was provided based on the refined first-order shear deformation theory, von-Karman geometric nonlinearity and the concept of the physical neutral plane. Secondly, the micro-element method, separation of variables method and Nayfeh and Emam’s method were applied to obtain analytical solutions for the critical condition, post-buckling configuration and buckling-vibration coupling natural frequency. Finally, the influence mechanism of factors such as pore distribution and gradient index on the critical condition, post-buckling configuration and buckling-vibration coupling natural frequency drift was studied. The results show that the instability type of PFGM sandwich beams transitions from bifurcation instability to snap-through under the effect of the gradient index. The variation pattern of the buckling-vibration coupled natural frequency also shifts from a V-shaped trend to a discontinuous jump, with the natural frequency exhibiting nonlinear behavior in the pre-buckling stage and single or double frequency jumps occurring in the post-buckling stage. These results are expected to provide new ideas and references for the design and regulation of PFGM structures.