Determination of natural frequencies of non‐uniform aluminum beams coated with functionally graded material

Abstract The present study comprises a numerical analysis used to find the dimensionless natural frequencies of non‐uniform aluminum beams coated with functionally graded material. The beams have variable width, and their variation is described by exponential and linear functions. While the coating material properties vary with a polynomial function, the lamination theory is used to calculate the overall properties of the functionally graded material coating. The beam is modeled as a modified Timoshenko beam and the gradual transition of the coating material properties as 25 layers of homogeneous isotropic material. In order to find the natural frequencies of the beam, finite element analysis was used, and the numerical results were processed with MATLAB, which were in good agreement with literature values. A parametric study is performed to study the effects of slenderness ( L/H ), coating thickness ( h/H ), skewness rate ( S ) and taper ratio ( w 2 /w 1 ) on the dimensionless natural frequencies. The study showed that tapering and skewing had a limited effect on the natural frequencies in general, however there exists a critical slenderness for every taper ratio and skewness rate where shape variation has a significant effect on the natural frequencies and should be considered.