Sen-Yung Lee1, Shueei-Muh Lin2,3, Kai-Ping Chang1
CMC-Computers, Materials & Continua, Vol.51, No.1, pp. 1-19, 2016, DOI:10.3970/cmc.2016.051.001
Abstract The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton's principle. These equations are expressed in terms of flexural and torsional displacements simultaneously. In this study, the analytical method is proposed. Firstly, two physical parameters are introduced to simplify the analysis. One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements. Based on the relation, the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms… More >
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