Vibration Analysis of Helicoidal Plates

Abstract

Governing equations for free vibrations of thin orthotropic or isotropic helicoidal plates are formulated by expressing displacements in terms of components in a helical orthogonal coordinate system. Equations derived for isotropic helicoidal plates are applied to the vibration problem of twisted rectangular turbine blades without camber. These twisted cantilever rectangular blades are simulated to be isotropic helicoidal plates with their angles of twist approximated to be their centre-line helical angles. Natural frequencies are calculated by solving the eigenvalue problem using the finite difference method and are compared to experimental measurements reported in the literature. Reasonably good agreement has been found for flexural modes; however, some discrepancies have also been observed for higher-order modes due to the inaccuracy of modelling the blade geometry as that of a helicoidal plate and due to the approximation of assuming the angle of twist to be the helical angle.