Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slenderness. | Journal of Science and Technology 54 (6) (2016) 785-796 DOI: UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM Nguyen Ngoc Huyen1, Nguyen Tien Khiem2, * 1 2 Thuy Loi University, 175 Tay Son, Dong Da, Hanoi Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi * Email: ntkhiem@; khiemvch@ Received: 21 January 2016; Accepted for publication: 20 September 2016 ABSTRACT Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slenderness. Keywords: FGM, Timoshenko beam; Modal analysis; Coupled vibrations. 1. INTRODUCTION The functionally graded material (FGM) that usually composes of metal and ceramic constituents has been proved to be an advanced composite compared to the layered ones. The fundamentals of manufacturing technology, modeling and analysis of that material were reviewed in [1 - 2]. Though the powerful methods such as finite element [3 - 5], dynamic stiffness [6] and spectral element [7] have been all developed for analysis of FGM structures, the analytical method has still remained the most efficient tool for dynamic analysis of beam-like FGM structures. Aydogdu and Taskin [8] have examined different high-order shear deformation theories by computing natural frequencies of simply supported functionally graded beam and shown that the classical beam theory gives higher results. Li [9] developed a theory of functionally graded Timoshenko beam neglecting the axial displacement
