Free Vibration of Axially Loaded Functionally Graded Porous Cracked Beams

This study employed a method of analysis to examine the free oscillation behavior of functionally graded (FG) porous-cracked beams under axial loads and varied boundary conditions. The cracked beam system was composed of interconnecting beam segments kept together by massless rotating springs. Based on the Timoshenko beam theory (TBT) or Euler–Bernoulli theories (EBT), each segment was sectionally flexible. Using a power-law function, mechanical features were expected to gradually change along with the height of the beam. Two different pore distributions, even and uneven, were also explored. Subsequently, Hamilton’s theory was used to derive the equations of kinematic motion for FG-cracked porous beams, and the transfer matrix (TMM) approach was used to get the determinantal equation. A parametric analysis was performed to evaluate how cracks, porosity distribution, slenderness ratio, volume fraction index, boundary conditions, and axial load affect the dynamic characteristics of FG beams. The results revealed that the suggested analytical approach provided several findings that were similar to the existing analytical outcomes in the literature. Moreover, the computer analysis demonstrated that porosity, especially when there were cracks, significantly affected the eigenfrequencies of FG beams. Hence, this study opened the door for possible applications in a variety of engineering settings by offering some crucial insights into the complex dynamics of FG porous-cracked beams.