Free vibration analysis of axially functionally Timoshenko beams with non-uniform cross-section
GE Ren-yu1, ZHANG Jin-lun1,JIANG Zhong-yu1,HAN You-min1,SUO Xiao-yong1,NIU Zhong-rong2
1.Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China
2.School of Civil Engineering, Hefei University of Technology, Hefei 230009, China
Non-uniform beams with varying axially material properties are widely used in civil, mechanical and aeronautical engineering, due to the fact that they can improve distribution of strength and weight, and guarantee the structural integrity. In this paper, an interpolating matrix method (IMM) for determining the natural frequencies orders of free transverse vibration of axially functionally graded Timoshenko beams is proposed. Firstly, based on the Timoshenko beam theory. the governing equations of free vibration analysis of axially functionally graded Timoshenko beams are transformed into a set of nonlinear characteristic ordinary differential equations with variable coefficients. Then, the interpolating matrix method (IMM) is adopted to solve the established equations, all the natural frequencies orders of free transverse vibration companying with the corresponding vibration mode functions of axially functionally graded beam were calculated at a time. Furthermore, the present methods do not pose any restrictions on both the type of material gradation and the variation of the cross section profile. and by comparing with the existing results of numerical examples, the validity of the present method is confirmed.
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