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Jun 22, 2026Keywords:
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Main Article Content
Analytical investigation of free vibrations in functionally graded material beams with different property distributions
Abstract
This study focuses on the analysis of the vibrational behavior of functionally graded material (FGM) beams, characterized by continuously varying mechanical properties along their thickness. Emphasis is placed on understanding the free vibrations of these structures and determining their eigenfrequencies using the Euler-Bernoulli beam model. The study considers several boundary conditions to evaluate the influence of material property variations on the beam’s dynamics. Three types of distributions are considered to describe the evolution of material properties: the power-law distribution (P-FGM), the exponential distribution (E-FGM), and the sigmoid distribution (S-FGM). This approach allows for a better understanding of the effect of each gradient type on the vibrational performance of the FGM beams and optimizes their design for various engineering applications. The principle of virtual work is applied to establish the equation of motion, and an eigenvalue problem is solved to determine the solutions. The comparison of numerical results with those found in the literature validates the proposed model, confirming its accuracy for the case of an E-FGM beam. Numerous studies are conducted to analyze the impact of the material property distributions on eigenfrequencies, considering various vibration modes and different boundary conditions.
