Sen Yung Lee1, Jyh Shyang Wu2
CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 133-154, 2009, DOI:10.3970/cmes.2009.040.133
Abstract The three coupled governing differential equations for the in-plane vibrations of curved non-uniform Timoshenko beams are derived via the Hamilton's principle. Three physical parameters are introduced to simplify the analysis. By eliminating all the terms with the axial displacement parameter, then reducing the order of differential operator acting on the flexural displacement parameter, 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 term of the angle of the rotation due to bending for the first time. The explicit relations between the axial and the flexural… More >
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