Dynamic analysis of a Francis turbine based on the fluid-structure interaction theorem

The dynamics equation for a Francis turbine blade in air and water was used to analyze blade fatigue failures caused by forced resonance.The finite element method was used to calculate the blade's natural frequencies in air and during various operating conditions and the influence coefficients which are related to data given in the literatures.The results indicate that the mode shapes in air are similar to those during operation,but that the blade's natural frequencies vary with the blade structure and the vibration modes.Therefore,the method can be used for resonance force analyses and the blade fatigue reliability designs.