The modified differential quadrature method (MDQM) is proposed for vibration analysis of elastically supported turbomachinery blades. A pre-twisted blade with varying cross-section is modelled as a Timoshenko beam. The blade is supported by two translational springs and three rotational springs at each end, and has a shroud that is modelled as a mass at the tip of the blade. The equations of motion and the boundary conditions for the coupled flexural and torsional vibration of the blade are obtained by using Hamilton's principle. Numerical results of elastically supported blades with or without a shroud are obtained by the MDQM and are validated by comparing with analytical solutions. Campbell diagrams for a pre-twisted blade with an airfoil cross-section are constructed. The accuracy and efficiency of the present approach have been demonstrated.
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