VIBRATION OF A FUNCTIONALLY GRADED TIMOSHENKO BEAM ON AN ELASTIC FOUNDATION DUE TO A MOVING MASS

In the past decade, beams that are made of functionally graded materials (FGM) have been employed in many engineering and biomedical application fields. In this paper, dynamic response of a FGM Timoshenko beam that is supported by an elastic foundation and is subjected to a moving mass, i.e., the effects of boundary flexibility, has been investigated. It is assumed that the material properties of the beam will change only in the thickness direction. The governing equations of motion are derived using Hamilton's principles. The partial governing differential equations of motion are reduced to a set of ordinary differential equations by using Petrov-Galerkin method. Runge-Kutta numerical scheme is employed to solve the obtained set of ordinary differential equations. After verification of the results for some special cases with known sloutions the effect of various parameters such as the velocity of moving loads, the boundary flexibility, the power-law index on the vibration of the beam have been investigated. The special case of the solution of the problem was compared with the study of Mesut Simsek [2010] and H. P. Lee [1998] which showed excellent agreement. The results have also been compared to the similar beam without FGM and the advantages of FGM have been discussed.