On the free vibration of a perforated Rayleigh beam with deformable ends

The development of perforation technology has increased the use of perforated structures in many engineering fields, from nano/micro to macro scales. This paper proposes a solution method to analyze the free vibration characteristics of perforated Rayleigh beams with both deformable and rigid boundary conditions and equal square holes along their vertical axes, modeled using elastic collapse springs at the beam ends. Using Rayleigh Beam Theory and an eigenvalue-based methodology using the Stokes transform and Fourier series, the research investigates the effects of parameters such as the number of holes, filling ratio, and boundary deformability on the vibration dynamics. The challenges associated with achieving rigid boundary conditions in actual engineering applications make it essential to examine the impact of deformable boundary conditions on the vibration characteristics of perforated beams. Key findings indicate that the number of perforations and boundary stiffness significantly influence the vibrational characteristics, which can be utilized to optimize the design and application of such beams in various engineering fields. Particularly noteworthy is the effect of symmetrical or asymmetrical variation of the stiffness parameters of the springs placed at the ends of the perforated beam on the vibration behavior. These results contribute to a deeper understanding of the dynamic behavior of perforated beams and provide practical insights for structural design.