Abstract
This paper focuses on the free vibration analysis of axially inhomogeneous and nonuniform beams considering the Bresse-Timoshenko slope-inertia model (BTSIM) as the governing equation. The BTSIM governing equation is obtained by modifying the rotational term in the kinetic energy expression. To solve the BTSIM equation analytically, it is reduced to an uncoupled second-order differential equation of Sturm-Liouville type with respect to rotation angle due to bending. This simplified equation is then solved to obtain closed-form solutions for some allowable variation of properties along the beam axis. Natural frequencies are then calculated for different material and geometric nonuniformities along the beam axis, and for various boundary conditions. A comparison between the results obtained for the reduced equation and the finite element method is carried out. The original and BTSIM model results are also compared with an available experimental result. The effect of changing the kinetic energy expression is shown by comparing the natural frequencies obtained from the original and BTSIM model for various boundary conditions.
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