Transfer matrix method for curved beam structures with a few branches in three-dimensional space

2020 ◽  
Author(s):  
Kei Nakanishi ◽  
Masayuki Arai ◽  
Kiyohiro Ito
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Curved Beam ◽  
Beam Structures ◽  
Three Dimensional Space

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).

Application of Transfer Matrix Method to Dynamic Analysis of Pipes With FSI

2014 ◽  
Author(s):  
Shuaijun Li ◽  
Bryan W. Karney ◽  
Gongmin Liu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Longitudinal Vibration ◽  
Three Dimensional ◽  
Structural Equations ◽  
Analytical Models ◽  
Pipe System ◽  
Various Boundary Conditions ◽  
Pipe Systems

Analytical models of three dimensional pipe systems with fluid structure interaction (FSI) are described and discussed, in which the longitudinal vibration, transverse vibration and torsional vibration were included. The transfer matrix method (TMM) is used for the numerical modeling of both fluidic and structural equations and then applied to the problem of predicting the natural frequencies, modal shapes and frequency responses of pipe systems with various boundary conditions. The main advantage of the present approach is that each pipe section of pipe system can be independently analyzed by a unified matrix expression. Thus the modification of any parameter such as pipe shapes and branch numbers does not involve any change to the solution procedures. This makes a parameterized analysis and further mechanism investigation much easier to perform compared to most existing procedures.

An Open Crack Model for Vibration Simulation of Beam Structures by Transfer Matrix Method

2007 ◽  
Vol 348-349 ◽  
pp. 893-896
Author(s):  
Ke Ming Wang ◽  
Song Xiang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Crack Detection ◽  
Vibration Monitoring ◽  
Crack Model ◽  
Open Crack ◽  
Element Analysis ◽  
Beam Structures ◽  
Stiffness Reduction

Crack detection of critical beam structures such as bridges and aircraft wings by vibration monitoring is based on understanding how a crack affects the vibration characteristics of a beam structure. Transfer matrix method is a convenient, effective, and hence widely used approach to beam vibration analysis, but a crack in the beam makes this method ineffective. This paper proposes an open crack model that simulates the local stiffness reduction effect of a transverse crack by a rectangular slot to make the transfer matrix method able to analyze vibrations of a cracked beam. The depth of the slot is identical to the depth of the crack, and the equivalent width of the slot is obtained by comparison of stiffness reductions of finite element analysis results and the counterpart transfer matrix method results. Different dimensions of rectangular beams, different crack positions and loading conditions are considered and statistic method is used to improve the generality and accuracy of the model. A calculation example of a cracked cantilever beam is given and the validity of the proposed model is verified with available results of existing models.

scholarly journals Transfer matrix method for elastic-plastic problem of space-curved beam structure

2019 ◽  
Vol 85 (874) ◽  
pp. 19-00026-19-00026
Author(s):  
Sho-ichi KURODA ◽  
Masayuki ARAI ◽  
Kiyohiro ITO
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Curved Beam ◽  
Beam Structure ◽  
Elastic Plastic
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