The method of discrete singularities in the problem of determining the frequencies and modes of vibrations of turbine blades

Abstract

The mathematical models for estimation of free vibrations of turbomachine elements in interaction with a fluid has been developed on the basis of the methods of potential theory as well as boundary singular and hypersingular integral equations. The analysis of plate vibrations with consideration of the effects of added liquid masses has been presented in the paper. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. The pressure is obtained by linearized Bernoulli integral. To evaluate a velocity potential, the system of singular boundary integral equations has been developed. The discrete singularities method has been used for its numerical solution.