Abstract:A method for bending vibration of variable cross-section beam was developed. Based on Timoshenko beam theory, the transverse oscillation equation of variable cross-section beam was derived, which allows the parameters, such as effective shear area, density, bending stiffness and moment of inertia, to vary in a manner of continuous and non-continuous related to axial coordinate. Then, the beam was modeled as a number of segments connected by continuity condition, and each segment was assumed to obey characteristic of uniform cross section. The relation of modal functions of contiguous segments was derived by using the conditions for continuity of displacement, slope of deflection curve, moment, and shear force at the connecting point between contiguous segments. Furthermore, the modal functions were determined for simply supported boundary conditions, and the natural frequencies can be obtained using Newton-Raphson method. To verify the effect of this method, the first third natural frequencies of a model were presented. The first three-order frequencies of a variable cross-section beam with the common boundary conditions were calculated by applying the new method introduced. The finite element results were adopted to verify the proposed method. Through the comparison with the results for Euler-Bernoulli beam model, it shows that the proposed method to solve the natural frequency of the beam with larges slenderness ratio has a better applicability.