Vibrations of Turbine Blades as Elastic Shells

Abstract

We consider vibrations of short turbine blades which have the length and the width of the same order of magnitude. We use the modern variant of the classical Kirchhoff shells based on Lagrange mechanics. The equations in components are derived from the tensor equations with account for the natural twist of the blade. We take displacement approximation with coefficients that are generalized coordinates of the Lagrange equations. The algorithm of calculations with computer mathematics is proposed; it includes evaluation of the generalized masses and stiffnesses. We present a benchmark example with the shell modal analysis.