Natural Vibrations of Geometrically Imperfect GRC Beam with Varying Boundaries in Contact with Fluid

This paper aims to investigate the natural vibration frequencies and corresponding vibration modes of a functionally graded (FG) graphene-reinforced composite (GRC) beam with geometric imperfections partially submerged in fluid. The primary objectives are to analyze the effects of Sine imperfections and varying boundary conditions on the vibration behavior.

The study employs the variable separation method to determine the fluid velocity potential and hydrodynamic loading. Circular graphene nanoplatelets (GPLs) are utilized to reinforce the host beam, considering both uniformly distributed (UD) and FG patterns. The effective Young’s modulus is computed using the 3D Halpin–Tsai model, while the Poisson ratio and mass density are determined through the rule of mixture. Governing equations are derived using the first-order shear deformation theory and Hamilton's principle. The solution is obtained through the differential quadrature (DQ) method with an iterative scheme.

Parametric analyses are conducted to assess the impact of GPL distribution pattern, fluid depth, and end supports on the free vibration behavior of GRC beam-fluid interaction systems. The findings highlight the significant influence of geometric imperfections on both the vibration frequency and mode of the GRC beam.

This study underscores the importance of considering geometrical imperfections in the analysis of GRC beam-fluid interaction systems. The results provide valuable insights into the effects of varying parameters on the vibration behavior, emphasizing the need for a comprehensive understanding of the dynamic response in practical applications.