Vibration analysis of elastically supported turbomachinery blades by the modified differential quadrature method

The modified differential quadrature method (MDQM) is proposed for vibratio n analysis of elastically supported turbomachinery blades. A pre-twisted bl ade with varying cross-section is modelled as a Timoshenko beam. The blade is supported by two translational springs and three rotational springs at e ach end, and has a shroud that is modelled as a mass at the tip of the blad e. The equations of motion arid the boundary conditions for the coupled fle xural and torsional vibration of the blade are obtained by using Hamilton's principle. Numerical results of elastically supported blades with or witho ut a shroud are obtained by the MDQM and are validated by comparing with an alytical solutions. Campbell diagrams for a pre-twisted blade with an airfo il cross-section are constructed. The accuracy and efficiency of the presen t approach have been demonstrated. (C) 2001 Academic Press.