Analytical evaluation of frequencies of bidirectional FG thick beams in thermal environment and resting on different foundation

This paper presents a theoretical study of the free vibration of functionally graded beam which has variable material properties along its length and thickness. These properties are also assumed to be temperature dependent. The beam is supposed to be simply supported and resting on several kinds of foundations. The governing equations are found analytically using a quasi 3D model that contains undetermined integral forms and involves few unknowns to derive. Navier's method is employed to determine and compute the vibration characteristics of bidirectional functionally graded (BDFG) beam on foundation. The accuracy of the present method for BDFG beam with temperature dependency has been validated. Then the effects of the grading indexes, geometrical properties, temperature dependent material properties, type of foundations and other parameters on the free vibration of BDFG beam are analyzed and discussed via a detailed parametric study.