| Summary: | 碩士 === 國立成功大學 === 機械工程學系碩博士班 === 100 === The three coupled governing differential equations for the out-of-plane vibrations of a non-uniform Timoshenko beam with variable curvature are derived via the Hamilton’s principle. Two physical parameters are introduced to simplify the analysis. By eliminating all the terms with the flexural displacement parameter, then reducing the order of differential operator acting on the angle parameter of the rotation due to bending, one uncouples the three governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in terms of the torsional angle for the first time. The explicit relations between the flexural displacement and the angle of the rotation due to bending and the torsional angle are also revealed. It is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms, then the exact solutions for the out-of-plane vibrations of a non-uniform Timoshenko beam with variable curvature can be obtained. Finally, the influence of the boundary conditions, the taper ratio, the slender ratio, the curvature parameter and the arc angle parameter on the curved beams is explored.
|
|---|
