Research on Energy Localization and Vibration Suppression of Axially Functionally Graded Porous Beams

Functionally graded porous beam (FGPB) structures are widely used in engineering due to their light weight, high strength, and vibration-damping performance. However, their energy localization and vibration suppression characteristics remain largely unexplored. To address this gap, this study proposes an axially functionally graded porous beam (AFGPB) structure capable of achieving energy localization and suppressing vibration transmission. A semi-analytical model is first developed within the Rayleigh-Ritz framework, using Gaussian functions as basis functions to accurately represent the displacement field. The accuracy of the model is validated by comparing its vibration characteristics with those obtained using the finite element method (FEM). Subsequently, the vibration behavior of double-AFGPB with simply supported boundary constraints is investigated. A series of numerical results are presented in this study to analyze the influence of porosity parameters on the energy localization effect and vibration suppression performance. Results reveal that the porosity power-law index N and truncation coefficient δ play key roles in energy localization and vibration suppression performance. When N ≥ 4, the energy localization effect and the vibration attenuation of the double-AFGPB become more pronounced with increasing N and decreasing δ, particularly in the low-frequency range.