scholarly journals Modified transfer matrix method for steady-state forced vibration: a system of beam elements*

2020 ◽  
Vol 69 (3) ◽  
pp. 235
Author(s):  
A Lahe
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Forced Vibration ◽  
Matrix Method ◽  
Beam Elements

Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

1980 ◽  
Vol 102 (1) ◽  
pp. 122-129 ◽  
Author(s):  
M. S. Darlow ◽  
B. T. Murphy ◽  
J. A. Elder ◽  
G. N. Sandor
Keyword(s):  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Critical Speed ◽  
Axial Direction ◽  
Matrix Analysis ◽  
Beam Elements ◽  
Conical Section ◽  
Rotor Model

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.

The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method

1993 ◽  
Vol 115 (4) ◽  
pp. 490-497 ◽  
Author(s):  
An-Chen Lee ◽  
Yuan-Pin Shih ◽  
Yuan Kang
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Three Dimensional ◽  
Continuous System ◽  
State Variables ◽  
Rotor Bearing ◽  
Steady State Responses ◽  
State Responses

A general transfer matrix method (GTMM) is developed in the present work for analyzing the steady-state responses of rotor-bearing systems with an unbalancing shaft. Specifically, we derived the transfer matrix of shaft segments by considering the state variables of shaft in a continuous system sense to give the most general formulation. The shaft unbalance, axial force, and axial torque are all taken into consideration so that the completeness of transfer matrix method for steady-state analysis of linear rotor-bearing systems is reached. To demonstrate the effectiveness of this approach, a numerical example is presented to estimate the effect of three-dimensional distribution of shaft unbalance on the steady-state responses by GTMM and finite element method (FEM).

Nonlinear Steady-State Rotordynamic Analysis Using Transfer Coefficient Method

1991 ◽  
Author(s):  
M. Kobayashi ◽  
S. Saito ◽  
S. Yamauchi
Keyword(s):  
Steady State ◽  
Transfer Coefficient ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Degrees Of Freedom ◽  
Computation Time ◽  
Squeeze Film ◽  
State Variables ◽  
Coefficient Method

Abstract This paper proposes a new method for steady-state, large-order nonlinear rotordynamic calculations: it uses a method called the transfer coefficient method (TCM), which is more convenient than the transfer matrix method. Since TCM calls for only the displacement as the independent variable, whereas both the displacement and the force are needed as the state variables in the conventional transfer matrix method, TCM promises a substantial saving of computation time without incurring loss in the accuracy of calculation. First, the outline of TCM is explained, then the nonlinear calculations for a rotor of many degrees of freedom are presented. This steady-state nonlinear calculation method is based on the discreet Fourier transform (DPT, FFT) and substructure synthesis. As an example, the nonlinear response due to unbalance mass is calculated and discussed in the case of the rotor which is supported by three bearings with two nonlinear squeeze film dampers.

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.

scholarly journals Investigation of the Steady-State Response of a Dual-Rotor System With Inter-Shaft Squeeze Film Damper

1985 ◽  
Author(s):  
Qihan Li ◽  
Litang Yan ◽  
James F. Hamilton
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Rotor System ◽  
Squeeze Film ◽  
Turbine Engine ◽  
Squeeze Film Damper ◽  
State Response ◽  
Unbalance Response

This paper presents an analysis of the steady-state unbalance response of a dual-rotor gas turbine engine with a flexible intershaft squeeze film damper using a simplified transfer matrix method. The simplified transfer matrix method is convenient for the evaluation of the critical speed and response of the rotor system with various supports, shaft coupling, intershaft bearing, etc. The steady-state unbalance response of the rotor system is calculated for different shaft rotation speeds. The damping effects of an intershaft squeeze film damper with different radial clearances under various levels of rotor unbalance are investigated.

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