| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 102 === The two coupled governing differential equations for the out-of-plane vibration of a non-uniform beam with variable curvature and the time dependent boundary conditions are derived via the Hamilton’s principle. With help of the shifting function method, the time dependent boundary conditions can be simplified. Two physical parameters are introduced to simplify the analysis. By reducing the order of differential operator acting on the torsional angle, one uncouples the two governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in terms of the flexural displacement parameter for the first time. The explicit relations between the flexural displacement 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 beam with variable curvature can be obtained. Finally, the influence of the coefficient of spring, the taper ratio, the slender ratio, the curvature parameter and the arc angle parameter on the curved beams is explored.
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