Abstract
This thesis presents the dynamic behaviour of a rotor consisting of multidiscs on a solid or hollow shaft, of the type used in gas or steam turbines. The effect of shaft flexibility on the dynamic characteristics of discs and the coupling effects between the discs and shaft modes are investigated. The influence of the disc flexibility on the hehaviour of single span and multispan shaft system is also investigated. A new, thick, three-dimensinnal, Isoparametric, cylindrical element is developed to determine the axial, bending and torsional modes and their coupling effects on the vibrating shaft-discs systems. The element is chosen to have eight nodes at its corners with twelve degrees of freedom at each node giving ninety-six degrees of freedom for a complete element. The triple integration over the element of stiffness and mass matrices are evaluated algebraically and numerically by Gaussian Quadrature using a 4 x 4 x 4 mesh. The main objective of the research reported in this thesis is to fulfil the requirement for a theoretical solution capable of accurate analysis, and the development of finite element program using a double precision arithmetic to obtain the dynamic characteristics of a multirotor system. The effect of disc flexibility on the dynamic characteristics of a system where the discs are carried in the interior of thin-walled cylindrical hollow shafts or "drums" are also studied. This type of disc-drum assemblies are used in aeroengines. Advantage of the rotational periodicity and linear periodicity of the wave propagation technique is fully utilised in the analysis. A new technique of combination of the two methodsis developed to investigate the dynamic behaviour of multidiscs - multi span systems. The present investigation is divided in two parts. The first part deals with several applications of the study of vibration characteristics of circular and annular discs, sector plates, cylindrical shells, hollow cylinders and shafts for various boundary conditions. The results for such applications are obtained separately by using the thick , three-dimensional element, and are compared with those of existing results given by classical plate and shell theory,by exact and other numerical methods of analysis. They also show very good agreement with the experimental results. The objective of this part is to present the accuracy of the thick, three-dimensional element solution including the effects of rotary inertia and shear deformation on the vibration characteristics in the case of axisymmetric and non-symmetric modes of vibration. The effect of the radii ratio b/a and thickness variation of uniform and variable thickness disc on the frequencies of vibration is discussed. The effect of sectorial angle 0 of the sector plate, the ratio of L/R[m], R[1]./R[o] and R[m]/t of the shaft on the dynamic behaviour are also studied. A thin, two-dimensional annular sector element with twelve degrees of freedom is also developed to find the mass and stiffness matrices and to obtain the frequencies of a uniform and variable thickness disc. A comparison between the results of vibrating disc obtained by the thick three-dimensional element and by this element is made to show the superiority of the thick, three-dimensional element to the thin, two-dimensional element for the dynamic analysis and also to find the influence of shear deformation and rotary inertia on the dynamic behaviour which is not allowed for in the thin plate theory. The large size of the stiffness and mass matrices obtained in the case of a three-dimensional cylindrical element analysis are reduced by using the eigenvalue economizer technique. The second part of this investigation is to present the coupling influence and interaction between the discs and the shaft by using the thick, three-dimensional element. Results presented for various cases with differing flexibility and geometry show clearly the coupling effects in a multi disc-shaft system. An inference diagram is developed from which the dynamic behaviour of a system can be predicted for differing flexibility relationships between the solid or hollow shafts and the discs. The effect of various fixing conditions and boundary conditions on the coupling characteristics are also presented. The effectiveness, simplicitiy of use and significance of the element applied and its superiority over other elements in the dynamic analysis is studied. The theoretical results show very close agreement with the experimental results.