An investigation into the numerical analysis of refined higher order shear deformation theory for frequency responses of two-directional functionally graded taper beams

For the aircraft and space shuttles to have the right properties, they need new engineering materials. Changing the qualities of the material in more than one direction is one way to do this. These features should be seen in in-plane, bi-directional functionally graded materials. This study examines the vibration behavior of a two-directional functionally graded taper beam (TDFGTB) with uniform load distribution. The analysis uses a refined higher-order shear deformation theory, Lagrange equations, and the displacement functions are formulated in simple algebraic polynomials incorporating admissible functions to satisfy the boundary conditions in both directions with the help of a Ritz-type solution. The components of admissible functions are derived from Pascal’s triangle. The study also examines the influence of taper ratios, aspect ratios, and gradation exponents on the vibration response. The results provide a benchmark for assessing beam theories and are crucial for optimizing the design of TDFGTBs.