Flexural vibration of rotating shafts by frequency domain hybrid modelling

Abstract In this paper the flexural vibration of a cantilevered rotating marine propeller is considered. From the transfer matrices of the distributed shaft and the lumped disc model, characteristic determinant of the distributed-lumped model of the system is derived. Direct search optimisation techniques are employed, enabling complex roots of the irrational characteristic determinant to be determined. Frequency response methods are used to determine the flexural response of the system. The discrete inverse Fourier transform technique is employed to compute the transient response from the frequency response data. Both the resonance and gyroscopic effects are identified. It is shown that by using frequency domain hybrid techniques, the system could be represented accurately by a reduced order model.

[1]  R. L. Ruhl,et al.  A Finite Element Model for Distributed Parameter Turborotor Systems , 1972 .

[2]  D. Durand,et al.  Estimation of electronic parameters of neurons using an inverse Fourier transform technique , 1992, IEEE Transactions on Biomedical Engineering.

[3]  An-Chen Lee,et al.  A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems , 1991 .

[4]  J. W. Lund,et al.  Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings , 1974 .

[5]  H. D. Nelson,et al.  The Dynamics of Rotor-Bearing Systems Using Finite Elements , 1976 .

[6]  A. Galip Ulsoy,et al.  Modal analysis of a distributed parameter rotating shaft , 1988 .

[7]  L. Meirovitch.  Analytical Methods in Vibrations , 1967 .

[8]  N. J. Fergusson,et al.  Frequency dependent element matrices for rotor dynamics analysis , 1992 .

[9]  Youn-sik Park,et al.  Non-linearity identification and quantification using an inverse fourier transform , 1991 .

[10]  H Bartlett,et al.  Distributed rotor dynamics , 1998 .

[11]  R. Stanway,et al.  Design and application of a finite element package for modelling turbomachinery vibrations , 1989 .

[12]  D. H. Hibner,et al.  Dynamic response of viscous-damped multi-shaft jet engines , 1975 .

[13]  W. Thomson.  Vibration Theory and Applications , 1966 .

[14]  R Whalley.  The Response of Distributed—Lumped Parameter Systems , 1988 .

[15]  R Whalley,et al.  The identification of engineering system parameters , 1997 .

[16]  B. D. Bunday,et al.  Basic optimisation methods , 1985, Mathematical Gazette.

[17]  Eric E. Ungar,et al.  Mechanical Vibration Analysis and Computation , 1989 .

[18]  R. Wooldridge,et al.  Advanced Engineering Mathematics , 1967, The Mathematical Gazette.

[19]  Edward W. Kamen,et al.  Fundamentals of signals and systems using MATLAB , 1997 .