The Riccati Transfer Matrix Method

1978 ◽  
Vol 100 (2) ◽  
pp. 297-302 ◽  
Author(s):  
G. C. Horner ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
New Technique ◽  
Computational Time ◽  
Structural Members ◽  
Rotating Shaft ◽  
Rotating Shafts ◽  
A New Technique ◽  
And Storage

The Riccati transfer matrix method is a new technique for analyzing structural members. This new technique makes use of an existing large catalog of transfer matrices for various structural members such as rotating shafts. The numerical instability encountered when calculating high resonant frequencies, static response of a flexible member on a stiff foundation, or the response of a long member by the transfer matrix method is eliminated by the Riccati transfer matrix method. The computational time and storage requirements of the Riccati transfer matrix method are about half the values for the transfer matrix method. A rotating shaft analysis demonstrates the numerical accuracy of the method.

A Direct Integration Technique for the Transient Analysis of Rotating Shafts

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388
Author(s):  
F. H. Chu ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Discrete Time ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transient Analysis ◽  
Direct Integration ◽  
Structural Members ◽  
Integration Technique ◽  
Continuous Space ◽  
Rotating Shafts

The continuous space discrete time Riccati transfer matrix method is a new direct integration technique for transient analysis of structural members. This method is applied to rotating shafts with bearing systems containing masses. Numerical results are given for a rotor with isotropic bearings.

A Direct Integration Technique for the Transient Analysis of Rotating Shafts

1981 ◽  
Vol 103 (1) ◽  
pp. 244-248
Author(s):  
F. H. Chu ◽  
W. D. Pilkey
Keyword(s):  
Transfer Matrix ◽  
Discrete Time ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Transient Analysis ◽  
Direct Integration ◽  
Structural Members ◽  
Integration Technique ◽  
Continuous Space ◽  
Rotating Shafts

The Continuous Space Discrete Time Riccati Transfer Matrix Method is a new direct integration technique for transient analysis of structural members. This method is applied to rotating shafts with bearing systems containing masses. Numerical results are given for a rotor with isotropic bearings.

A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Yuan Kang ◽  
An-Chen Lee ◽  
Yuan-Pin Shih
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Harmonic Balance Method ◽  
Continuous System ◽  
Euler Beam ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Steady State Responses

A modified transfer matrix method (MTMM) is developed to analyze rotor-bearing systems with an asymmetric shaft and asymmetric disks. The rotating shaft is modeled by a Rayleigh-Euler beam considering the effects of the rotary inertia and gyroscopic moments. Specifically, a transfer matrix of the asymmetric shaft segments is derived in a continuous-system sense to give accurate solutions. The harmonic balance method is incorporated in the transfer matrix equations, so that steady-state responses of synchronous and superharmonic whirls can be determined. A numerical example is presented to demonstrate the effectiveness of this approach.

An Improved Transfer Matrix Method for Steady-State Analysis of Nonlinear Rotor-Bearing Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 303-310 ◽  
Author(s):  
J. W. Zu ◽  
Z. Ji
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Roller Bearing ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Rotating Shaft ◽  
Damping Characteristics ◽  
Rotor Bearing

An improved transfer matrix method is developed to analyze nonlinear rotor-bearing systems. The rotating shaft is described by the Timoshenko beam theory which considers the effect of the rotary inertia and shear deformation. A typical roller bearing model is assumed which has cubic nonlinear spring and linear damping characteristics. Transfer matrices for the Timoshenko shaft element, disk element, and nonlinear bearing element are derived and the global transfer matrix is formed. The steady-state response of synchronous, subharmonic, and superharmonic whirls is determined using the harmonic balance method. Two numerical examples are presented to demonstrate the effectiveness of this approach.

A Hybrid Method for the Vibration Analysis of Rotor-Bearing Systems

1991 ◽  
Vol 205 (2) ◽  
pp. 131-137 ◽  
Author(s):  
R Firoozian ◽  
H Zhu
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Hybrid Method ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Mode Shapes ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Rotor Bearing

The transfer matrix method together with a digital computer form the foundation of the dynamic analysis of rotor-bearing systems. The properties of each segment of the rotating shaft are expressed in simple matrix form and the overall dynamic behaviour is then obtained by successive multiplication of the element matrices. The main drawback associated with this method is the numerical instability in calculating natural frequencies for complex systems. The finite element method, on the other hand, uses the element stiffness and mass matrices to form the global equation of motion for the complete system. This avoids the numerical problems of the transfer matrix method at the expense of the computer memory requirements. The new method described in this paper combines the transfer matrix and finite element techniques to form a powerful algorithm for vibration analysis of rotor-bearing systems. It is shown that the accuracy improves significantly when the transfer matrix for each shaft segment is obtained from finite element techniques. The accuracy and efficiency of the hybrid method are compared with the transfer matrix method for a simply supported uniform rotating shaft where an analytical solution for the critical speeds and mode shapes is available. The method is then applied to a flexibly supported uniform shaft and a non-uniform shaft with a large disc to show the capability of the method for finding the critical speeds of complex rotor-bearing systems.

Sign in / Sign up

Export Citation Format

Share Document