Meshless local Petrov-Galerkin method for rotating non-uniform axially functionally graded beam

This study investigates the dynamic behaviour of rotating axially functionally graded (AFG) beams, both uniform and non-uniform, using the Meshless Local Petrov-Galerkin (MLPG) method. AFG beam composed of aluminium and zirconia is considered, with aluminium distributed at the left end and zirconia at the right end of the beam. For the accuracy first- five natural frequencies, minimum seven nodes are required in one sub domain. For numerical integration 10-point Gauss-Legendre integration scheme are used for one sub-domain. Chebyshev orthogonal polynomials have been employed as the basis functions in the present MLPG formulation. The effect of rotational speed on natural frequencies is analysed, revealing that increasing rotational speed leads to higher frequencies due to centrifugal stiffening. Non-uniform beams exhibit slightly higher natural frequencies than uniform beams due to their varying mass and stiffness distributions. The study further explores material gradation through exponential and power-law functions. Additionally, effects of tapering and boundary conditions on the natural frequencies are also examined, with C-C beams exhibiting the highest frequencies, while H-H and C-F beams show comparatively lower values. Mode shape analysis highlights asymmetric bending in C-F beams and symmetric deformation in C-C beams, while simply supported beams (H-H) display classical sinusoidal patterns. The effect of material non-homogeneity on natural frequencies is also examined for various boundary conditions, for C-F conditions increasing non-homogeneity parameter (n) from 0 to 2 results in increase in lower mode frequencies whereas for C-C, H-H, C-H conditions the natural frequency decreased with increasing non-homogeneity. Results are verified from existing literature.