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ABSTRACT:In this paper, a numerical method is employed to study the free vibration of axially loaded composite Timoshenko beam. The problem is governed by a set of coupled second-order ordinary differential equations of motion, under different boundary conditions. The method is based on numerical integration rather than the numerical differentiation since the highest derivatives of governing functions are chosen as the basic unknown quantities. The kernels of integral equations turn out to be Green's function of corresponding equation with homogeneous boundary conditions. The accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature. It is shown that good accuracy can be obtained even with a relatively small number of nodes.