Application of Transfer Matrix Method to Analysis of Transient Response of Beam

1987 ◽  
Vol 109 (3) ◽  
pp. 248-254 ◽  
Author(s):  
Moriaki Goya ◽  
Takuo Hayashi ◽  
Koichi Ito ◽  
Hiroshi Ohki
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Nonlinear Differential Equations ◽  
Effective Means ◽  
Linear Equations ◽  
Elastic Beam ◽  
Transient Responses ◽  
Concentrated Mass ◽  
Finite Difference Equations

The transient responses of an elastic beam to large dynamic deformations were analyzed numerically, using the transfer matrix method. Geometrically nonlinear differential equations were linearized by introducing increments of unknown functions, and the resulting linear equations were approximated by finite difference equations. A field transfer matrix was introduced for the analyses of large deformations; this determined the relationship between the incremental state vectors at both ends of the elastic segments. The Newmark β formulation was chosen to approximate the equation of motion for concentrated masses. A concentrated mass point transfer matrix and an inhomogeneous vector were introduced for analyses of the transient responses of the beams. A superposition scheme for the transfer matrix method was proposed as an effective means of obtaining a solution satisfying the boundary conditions at both ends of the beam.

The Analysis of Natural Characteristics of Pipeline Structure Systems Based on Frequency-Domain Transfer Matrix Method

2011 ◽  
Vol 383-390 ◽  
pp. 4541-4545
Author(s):  
Xiao Di Wu ◽  
Gong Min Liu ◽  
Hao Chen
Keyword(s):  
Frequency Domain ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Pipeline System ◽  
Computational Results ◽  
Concentrated Mass ◽  
Bent Pipe ◽  
Natural Characteristic ◽  
Domain Transfer

A pipe structure model composed of straight pipe, bent pipe, concentrated mass and flexible support was established. The axial, lateral and circumferential vibration of this model were taken into account in the paper. Then it was realized to calculate the natural characteristic of this pipeline in computer by using MATLAB language to program a series of procedures based on frequency-domain transfer matrix method. The calculation results were compared with the ANSYS simulation results, which illustrated the upper accuracy of frequency-domain transfer matrix method in calculating natural characteristic problems of pipeline structure system. At last, The pipeline system was analyzed with experimental modal method．By comparing the experimental results and computational results, relatively lesser error showed that computational results were reliable and frequency-domain TMM was verified to be valuable for practical application.

An Increment Transfer Matrix Method for the Torsional Vibration Response of Steam Turbo-Generator Shaft System

2010 ◽  
Vol 34-35 ◽  
pp. 1082-1087 ◽  
Author(s):  
Cheng Bing He ◽  
Cheng Xing ◽  
Jian Shen
Keyword(s):  
Transfer Matrix ◽  
Torsional Vibration ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Short Circuit ◽  
Nonlinear Differential Equations ◽  
Mass Model ◽  
Shaft System ◽  
Turbo Generator ◽  
Generator Unit

In order to solve nonlinear system torsion response of turbo-generator unit, an increment transfer matrix method based on step-by-step integration method and traditional transfer matrix method was put forward. The method can be directly used to analyze nonlinear differential equations. Combined with Riccati method, the increment transfer matrix method was used in a multi-mass model. And matrix equations calculating the responses of torsional vibrations were deduced. Torsional vibration resulted from the faults of short circuit and asynchronous synchronization of 600MW steam turbo-generator unit were discussed in this work by using the increment transfer matrix method which can also extend the application of transfer matrix method in nonlinear field.

scholarly journals Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pengfei Liu ◽  
Hongjun Liu ◽  
Qing Wu
Keyword(s):  
Transfer Matrix ◽  
Timoshenko Beam ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Elastic Beam ◽  
Vibration Characteristics ◽  
Bernoulli Beam ◽  
Flexible Wheelset ◽  
Euler Bernoulli Beam

The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

scholarly journals Modelling of Critical Velocities of the Cardan Mechanism using Transfer Matrix Method

2021 ◽  
Vol 23 (1) ◽  
pp. B33-B38
Author(s):  
Petr Hrubý ◽  
Tomáš Náhlík
Keyword(s):  
Mechanical Properties ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Physical And Mechanical Properties ◽  
Transfer Matrices ◽  
Concentrated Mass ◽  
Method Transfer ◽  
Eigen Frequencies ◽  
Critical Velocities

The presented paper focuses to rotating components of mechanical constructions. The problem of the spatial combined bending-gyratory vibration and calculation of the Eigen frequencies is studied. The model of Cardan Mechanism is solved by the transfer matrix method. Transfer matrices were derived for shaft, concentrated mass and elastic bearing. The physical and mechanical properties of each part of the mechanism are hidden in these matrices. A procedure for calculating Eigen frequencies was proposed.

Natural vibration characteristics determination of elastic beam with attachments based on a transfer matrix method

2021 ◽  
pp. 107754632098064
Author(s):  
Dongyang Chen ◽  
Chaojie Gu ◽  
Minjiao Li ◽  
Bowen Sun ◽  
Xiaoyin Li
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Multibody System ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Vibration Characteristics ◽  
Boundary State

The transfer matrix method for multibody system takes into account the accuracy of the equations of motion and the efficiency of the algorithm. Especially if a system is composed of flexible and rigid components, transfer matrix method for multibody system reduces the dynamics problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundary are made up of rotation angles, displacements, shear forces, and bending moments, which are normally half known and half unknown. The proposed transfer matrix method for multibody system of multibody system dynamics to determine the vibration characteristics is easy to formulate, systematic to apply, and simple to code. The purpose of this study is to introduce a modeling and simulation idea of beam with attachments based on transfer matrix method for multibody system. Numerical results for several examples of beam with attachments are presented to demonstrate the validity of this method.

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