Mechanics of functionally graded beams: analytical, computational, and experimental analyses

Abstract Bending and vibration (modal) analyses of a functionally graded beam are proposed. Analytical, computational, and experimental results are obtained and compared. The functionally graded beam is modeled according to Euler- Bernoulli beam theory. The power-law rule is assumed to show the functional gradation of the beam. Displacement fields and energy expressions are given. Hamilton’s principle is used to derive the equation of motion. Firstly, free vibration analysis of the functionally graded Euler–Bernoulli beam is investigated. Natural frequencies and mode shape expressions are analytically obtained for four support conditions. Secondly, a novel computational model is constructed using the finite element method based Ansys Workbench software. The new approach allows the simulation of exact continuous variation of material gradation. Finally, the experimental process is presented. The functionally graded beam is manufactured with 3-D printing technology using the additive manufacturing method. PETG/CF and PLA polymer materials are utilized to manufacture the test samples. Bending and vibration tests are done. The experimental results are compared with analytical and computational results. The effects of the power law index on the bending displacements and natural frequencies of the functionally graded beam are shown. The analytical and computational results are close to those of the experimental ones. Consistency of analytical computational and experimental results is proposed. The results show that the error percentages are very low compared to existing works.