CONTENTS

INTRODUCTION

Linear rotordynamics

Nonlinear rotordynamics

Nonstationary rotordynamics

Time-domain versus frequency domain

PART I: BASIC TOPICS

JEFFCOTT ROTOR

Undamped Jeffcott rotor

Complex coordinates in rotordynamics

Jeffcott rotor with shaft bow

Jeffcott rotor with viscous damping

Jeffcott rotor with structural damping

Jeffcott rotor with nonsynchronous damping

Effect of the compliance of the bearings

Rotor-fixed coordinates

Stability in the supercritical field

Drag torque at constant speed

MODEL WITH FOUR DEGREES OF FREEDOM: GYROSCOPIC EFFECT

Generalized coordinates and equations of motion 

Uncoupled gyroscopic system

Free whirling of the coupled, undamped system 

Response to unbalance and shaft bow 

Frequency response 

Unbalance response: modal computation 

Modal uncoupling of gyroscopic systems 

DISCRETE MULTI-DEGREES-OF-FREEDOM ROTORS 

Transfer matrices approach: the Myklestadt-Prohl method 

Lumped parameters stiffness method 

The finite element method

Real versus complex coordinates

Fixed versus rotating coordinates

Complex state space equations

Static solution

Computation of the unbalance response

Plotting the Campbell diagram and the roots locus

Reduction of the number of degrees of freedom

CONTINUOUS SYSTEMS: TRANSMISSION SHAFTS 

The Euler-Bernoulli vibrating beam.

Other boundary conditions

Effect of the moments of inertia: Timoshenko beam

Dynamic stiffness matrix

ANISOTROPY OF ROTORS AND SUPPORTS

Isotropic rotors on anisotropic supports

Nonisotropic rotors on isotropic supports

TORSIONAL AND AXIAL DYNAMICS

Torsional free vibration

Forced vibrations

Torsional critical speeds

Axial vibration

ROTOR-BEARINGS INTERACTION

Rigid body and flexural modes

Linearization of the characteristics of the bearings

Rolling elements bearings

Fluid film bearings

Magnetic bearings

Bearing alignment in multi-bearing rotors

PART II - ADVANCED TOPICS

ANISOTROPY OF ROTORS AND SUPPORTS

Nonisotropic Jeffcott rotor

Equation of motion for an anisotropic machine with many degrees of freedom

NONLINEAR ROTORDYNAMICS

Nonlinear isotropic Jeffcott rotor

Nonlinear isotropic Jeffcott rotor running on nonsymmetric supports

Nonlinear anisotropic Jeffcott rotor running on symmetric supports

Systems with many degrees of freedom

NONSTATIONARY ROTORDYNAMICS

Nonstationary linear Jeffcott rotor

Nonstationary general Jeffcott rotor

Nonstationary rotor with 4 degrees of freedom

Generic, torsionally stiff, multi degrees of freedom, system

Blade loss

DYNAMIC BEHAVIOR OF FREE ROTORS

Single-rigid-body rotor

Large amplitude whirling of a linearily-constrained rigid rotor

Twin-rigid-bodies free rotor

Multi-body free rotors

DYNAMICS OF ROTATING BEAMS AND BLADES

Rotating pendulum

Rotating pendulum constrained to oscillate in a plane

Spring-loaded rotating pendulum

Rotating string

Dynamics of a row of rotating pendulums

Interaction between the dynamics of the blades and the dynamics of the shaft

DYNAMICS OF ROTATING DISCS AND RINGS

Rotating membranes

Rotating circular plate

Disc-shaft interaction

Uncoupled modes

Vibration of rotating circular rings

Vibration of thin-walled, rotating, cylinders

Instability of rotating, cylinders partially filled with liquid

THREE DIMENSIONAL MODELING OF ROTORS

Symmetry of the rotor

Simplified FEM elements for thin bladed discs modelling

General finite element discretization

Equation of motion in the inertial frame

Axi-symmetrical annular elements

Axi-symmetrical shell element

Brick elements

DYNAMICS OF CONTROLLED ROTORS

Open loop equations of motion

Closed-loop equations of motion

Rigid rotor on magnetic linearized bearings

Modal control of rotors

APPENDICES

VECTORS, MATRICES AND EQUATIONS OF MOTION

AN OUTLINE ON ROTOR BALANCING

ROTORDYNAMICS VIDEOS

DYNROT LIGHT ROTORDYNAMICS CODE

BOOKS ON ROTORDYNAMICS

REFERENCES

INDEX

This comprehensive book deals with the theory of dynamics of rotating systems. … The author attempts to model the dynamic behaviour of all rotating bodies, including not only shafts and turbine motors but also rotating blades and flexible spinning spacecraft. … Without hesitation, this book is recommended to researchers and engineers whose work involves modelling and analysis of rotating systems. The book is definitely a valuable text for graduate students studying rotor dynamics and for those pursuing their own novel approaches."

International Journal of Acoustics and Vibration, Vol. 10 (4), 2005