Abstract
A rational method and an associated digital computing capability are developed for the generalised and detailed analysis of torsional vibration characteristics of machinery installations, particularly those modern marine systems having branched configurations. The proposed method caters for the application of many discrete sources of applied harmonic excitation and forms of damping, and determines the characteristic responses of lumped-inertia systems over frequency ranges related to harmonic orders of shaft speeds. The theoretic approach attaches great importance to the routine investigatory requirements of the practising vibration analyst as an engineer rather than as a mathematician. Consequently, although based on classical solution, the derivation of the method places emphasis on simplicity in theory and mathematics, consistency in notation and conventions, and physical realism in the concepts of equivalent organisational modelling of branched installations. Furthermore, the general organisation of problem solution and the presentation of results closely follow the familiar Holzer tabulation format. As an essential complanent to the main work, an advanced computing capability for torsional natural frequency and normal modal analysis is presented, which is eminently suitable for branched system treatment, is completely automatic, and fully exploits the power of the modern digital computer. This method for natural frequency solution is developed from the Holzer trial procedure, making use of the Rayleigh Principle concerning equation of energies, in conjunction with a successive modal-component extraction technique. The validity of the forced-damped method developed for digital computer application is supported and confirmed in all essential respects by a completely independent approach to solution, making extensive practical use of analogue computer analytical techniques. The latter phase of research spotlights some neglected areas of vibration study and discloses an essential key to a fundamentally more general method for vibration analysis, employing direct integration, for future development.