Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method

In this paper, an analytical method is developed to study the dynamic behavior of functionally imperfect Euler-Bernoulli and Timoshenko graded beams with differing boundary conditions, namely, hinged-hinged, clamped-clamped, clamped-hinged, and clamped-free. A transfer matrix method is used to obtain the natural frequency equations. The modified rule of mixture is used to describe the material properties of the functionally graded beams having porosities. The porosities are assumed to be evenly distributed over the beam cross-section. In this study, the effects of boundary conditions, material volume fraction index, slenderness ratio, beam theory, and porosity on natural frequency are determined. The present results are validated with results available in the literature.