Vibration Analysis of Rotating Cambered Helicoidal Turbomachine Blades

Abstract

A procedure for the vibration analysis of rotating cambered helicoidal blades using curved shell finite element based on Mindlin theory is given. The strain displacement relations of Gol den'veizer are used in the development of a thick doubly curved helicoidal 'shell element including initial in-plane stress effect The method is applied to rotating cambered prehvisted blades. F.g. I Rotating Turbine Blade

A Mixed Shell Element for Cambered Helicoidal Blades and Dynamic Stresses due to Aerodynamic Excitation

“…2. The coefficients of first quadratic form A, B, C and the radii of curvature R1,R2,R12 for a shallow shell can be determined easily, see Rao (1991) and Rao et. al.…”

“…1 1 1 The kinetic energy of the element can be shown to be, see Rao et al (1997) T= TI +T2 +T3 (14) where a9,,,+hh,CO,,,) [(aO,,,+h,,,) (-a9,,, +h,,, -hh, ^0,,,)…”

“…Ritz method is applied for rotating pre-twisted flat blades by Petricone and Sisto (1970), Gupta and Rao (1987), however, constant width, thickness and radius of curvature are assumed. A procedure for the rotating cambered helicoidal blades using curved shell element based on Mindlin (1951) shell theory is presented by Rao et al (1997). Here, an eight noded mixed shell element based on Reissner's functional is presented, following the pattern of Noor and Andersen (1982) so that the stresses can be evaluated in an accurate manner.…”