Abstract
The free vibration of beams with variable cross-section was investigated. The governing equations for beams with variable cross-section were obtained using Timoshenko beam theory. The effect of axial and shear deformations, rotary inertia and non-uniformity cross-section were considered in the formulations. Ordinary differential equations in scalar form obtained in the Laplace domain were solved numerically using the complementary functions method. The free vibration of beams with variable cross-section was analysed. The effects of non-uniformity parameter, boundary conditions on free vibration were investigated. The results obtained in this study were found to be in good agreement with those obtained from ANSYS. Keywords: Free vibration, non-uniform beams, complementary function method
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