Study On Dynamic Characteristics Of Rotating Thin-walled Cylindrical Shells

To achieve lower weight and higher strength, cylindrical shells are widelyused in practical engineering. In steam turbine engines, advanced gas turbines,aircraft jet engines and other rotating machinery, lots of their core componentsutilize thin-walled cylindrical shells, such as drums of drum-disk type rotors,high-speed rotating shafts and labyrinth gas seals of the aircraft engines. Whenthe rotating machinery works, those thin-walled cylindrical shells rotate at thesame speed as the machinery. Unlike non-rotating cylindrical shells, Coriolis andcentrifugal forces as well as the hoop tension due to rotation have significantinfluence on the dynamic behavior of rotating cylindrical shells. Thus, it is ofgreat interest to conduct some researches to improve the understanding ofvibrational characteristics of rotating cylindrical shells.In this dissertation, free vibration and dynamic response of rotating thin-walled cylindrical shells are investigated in detail by analytical and numericalapproaches. Further, a series of studies are performed for the drum in turbomachinery which can be seen as a practical application of rotating cylindricalshells. The main achievements derived in this dissertation are listed as follows.An exact method and an approximate approach are presented for thevibration characteristics of thin rotating cylindrical shells with various boundaryconditions by use of Fourier series expansion method and wave propagationapproach, respectively. The validation studies show that the Fourier seriesexpansion method presented makes it possible to derive an exact solution for athin rotating cylindrical shell with classical boundary conditions of any typeprovided that convergence of the series can be guaranteed. It can also beobserved that the wave propagation approach is more suitable for the vibrationanalysis of rotating cylindrical shells with larger length-to-radius ratio and ismore accurate for traveling modes with higher circumferential wavenumber.Moreover, using the Fourier series expansion method, vibration characteristics ofthin rotating cylindrical shells with four kinds of boundary conditions, namely,clamped–clamped, clamped-free, clamped-simply supported and simplysupported–simply supported boundary conditions, are investigated and theinfluence of boundaries on the vibration characteristics is also discussed. The Rayleigh-Ritz method is employed to derive the frequency equations ofrotating cylindrical shells with elastic constraints by taking the characteristicorthogonal polynomial series as the admissible functions and utilizing artificialsprings to simulate the elastic constraints. Convergence and accuracy studiesshow that the method proposed here is a relative convenience and efficientmethod dealing with vibration analysis of rotating cylindrical shells witharbitrary edges. Based on this method, the variation of the travelling wavefrequencies with respect to the stiffness of the connection joint is depicted in th isdissertation.An analysis is presented for the forced vibration analysis of thin rotatingcylindrical shells with various boundary conditions. Then, the approach proposedis applied to investigate the vibration characteristics of a clamped-clamped thinrotating cylindrical shell subjected to a harmonic point load and a constant pointload in the transverse direction, and the results and discussions are presented.Taking into account the coupling of rotor whirl and drum vibration, thedynamic model of a disk-drum-shaft system is established for the drum-disk typerotors in turbo-machines. Based on this model, the effect of the unbalanced rotorwhirl and rub-impact between disk and stator on drum vibration is studied in thisdissertation. The results show that the unbalanced rotor whirl is coupled with thedrum vibration modes which carry one circumferential wavenumber. If thesupport stiffness of the shaft is linear, the centroid motion locus of the shaft willbe a circle and the steady-state vibration cannot be maintained. However, thecentroid motion locus will be complex provided that the support stiffness of theshaft is nonlinear. Under this circumstance, slight and steady-state vibration ofdrum will be induced by the whirl of the unbalanced rotor. In addition, due to thecoupling of rotor whirl and drum vibration, the variation of stiffness ratio,friction coefficient or clearance can lead to complex nonlinear behavior in thedynamical response of the drum.