Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams

In the present study, effects of material non-homogeneity and two-parameter elastic foundation on the fundamental frequency parameters of the simply supported beams are examined. Material non-homogeneity is characterized taking into account the parabolic variations of Young's modulus and density along the thickness direction of the beam while the value of Poisson's ratio is assumed to remain constant. The foundation medium is assumed to be linear, homogeneous and isotropic, and it is modeled by the Pasternak model with two parameters for describing the reaction of the elastic foundation on the beam. At first, the equation of the motion including the effects of the material non-homogeneity and two-parameter elastic foundation is provided. Then, the solutions including fundamental frequency parameters versus various non-homogeneity, density and foundation parameters, and length to depth ratio adopting the Timoshenko beam theory as well as the Euler-Bernoulli beam theory are presented. To show the accuracy of the present results, a comparison is carried out and a good agreement is found.