Abstract
The purpose of this thesis is to analyse the vibration characteristics of aerofoil cross-section straight and pretwisted blades and blade packets on infinitely rigid discs and blades and shrouded blades on flexible discs under rotating conditions using the finite element method. In the first part of the thesis the analysis of a rotating aerofoil cross-section blade is carried out by assuming that the blade is fixed at the periphery of an infinitely rigid disc rotating at a constant angular velocity. The effect of pretwist, stagger angle, rotational speed and the distance of shear centre from the centroid on the vibration characteristics is investigated. A finite element model is developed to analyse the vibration characteristics of an asymmetric cross-section tapered beam. The assumption made is that the variation of the cross-sectional properties along the element which is given by the Chebyshev polynomial is approximated by a quadratic polynomial. This element is applicable for the analysis of variable cross-section beam whose cross-sectional properties are defined at some discrete points along the blade length. To investigate the behaviour of blade packet on infinitely rigid discs and shrouded blades on flexible discs the shroud is assumed to have a constant curvature and is analysed by using curved beam finite elements. Two in-plane and one out-of-plane curved beam elements with an internal node at the mid-point of each element are developed. It is shown that the element with internal node converges faster than the element without internal node. The effects of stagger angle, shroud thickness, shroud width, rotational speed, disc radius, and the distance of shear centre from the centroid on the vibration characteristics of straight and pretwisted blade packets are investigated. In the case of straight packets an internal node is assumed at the mid-point of each blade element and it is shown that by the introduction of an internal node the overall matrix size and consequently the computing time of the problem is reduced markedly. Various tests of straight and pretwisted aerofoil cross-section blade packets are also carried out. Finally the effect of the disc flexibility on the vibration characteristics of straight or pretwisted blades and shrouded blades under rotating and non-rotating conditions is considered. To reduce the size of the matrix the finite element method is used in conjunction with wave propagation technique and cyclic symmetry. For the first time the variation of phase difference between the bendings and torsional modes along the blade length of pretwisted and straight bladed-disc is illustrated. The effects of pretwist, stagger angles, distance of shear centre from the centroid and rotational speed on the vibration characteristics of bladed discs and shrouded-bladed-discs are investigated. A series of tests of the disc, staggered, pretwisted-bladed-disc and shrouded-bladed-discs are carried out. Experimentally observed mode shapes are compared with the theoretical mode shapes. Furthermore the dynamic characteristics of an assembly of twenty, two-bladed packets on elastic disc is investigated and it is shown that the vibration characteristics of the assembly can be estimated from the independent vibration characteristics of blade packet and that of the disc.