Study of New Guidelines for Material Distribution in Vibrating AFG Beams

Abstract

The free transverse vibrations of axially functionally graded (AFG) beams with two classic boundary conditions are studied. The distinctive qualities of this class of advanced materials acquire greater importance when the resistant element is in vibratory environments in which the inertial effect can be decisive. The classical Bernoulli-Euler theory is adopted to describe the flexural behavior of the beam. Due to the analytical difficulties, governing equations with variable coefficients, their solution is normally approached by approximate methods. This has motivated the subject to be approached mainly from a mathematical perspective, emphasizing the analysis on the numerical and analytical tools that lead to its solution. This mathematical approach also includes the distribution of the constituent materials. In the present work the composition of the FG material according to engineering criteria based on the structural behavior of the beam is proposed. The problem is solved by applying the approximate methods of Rayleigh-Ritz. A variety of numerical examples are evaluated with different variations in material composition. Dynamic stiffening effect is achieved and discussed. The results agree with particular situations of the model, available in the scientific literature.