• Title, Summary, Keyword: Transfer Matrix Method

### Vibration analysis of rotating beam with variable cross section using Riccati transfer matrix method

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.199-207
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• 2019
• In this paper, a semi-analytical method will be discussed for free vibration analysis of rotating beams with variable cross sectional area. For this purpose, the rotating beam is discretized through applying the transfer matrix method and assumed the axial force is constant for each element. Then, the transfer matrix is derived based on Euler-Bernoulli's beam differential equation and applying boundary conditions. In the following, the frequencies of the rotating beam with constant and variable cross sections are determined using the transfer matrix method in several case studies. In order to eliminate numerical difficulties in the transfer matrix method, the Riccati transfer matrix is employed for high rotation speed and high modes. The results are compared with the results of the finite elements method and Rayleigh-Ritz method which show good agreement in spite of low computational cost.

### An Analysis of Cylindrical Tank of Elastic Foundation by Transfer Matrix and Stiffness Matrix (전달행렬과 강성행렬에 의한 탄성지반상의 원형탱크해석)

• 남문희;하대환;이관희;장홍득
• Computational Structural Engineering
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• v.10 no.1
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• pp.193-200
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• 1997
• Even though there are many analysis methods of circular tanks on elastic foundation, the finite element method is widely used for that purpose. But the finite element method requires a number of memory spaces, computation time to solve large stiffness equations. In this study many the simplified methods(Analogy of Beam on Elastic Foundation, Foundation Stiffness Matrix, Finite Element Method and Transfer Matrix Method) are applied to analyze a circular tank on elastic foundation. By the given analysis methods, BEF analogy and foundation matrix method, the circular tank was transformed into the skeletonized frame structure. The frame structure was divided into several finite elements. The stiffness matrix of a finite element is related with the transfer matrix of the element. Thus, the transfer matrix of each finite element utilized the transfer matrix method to simplify the analysis of the tank. There were no significant difference in the results of two methods, the finite element method and the transfer matrix method. The transfer method applied to a circular tank on elastic foundation resulted in four simultaneous equations to solve completely.

### Free Vibration Analysis of Double Cylindrical Shells Using Transfer of Influence Coefficent (영향계수의 전달에 의한 2중 원통형 셸의 자유진동해석)

• Choi, Myung-Soo;Yeo, Dong-Jun
• Journal of Power System Engineering
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• v.21 no.5
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• pp.48-54
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• 2017
• The transfer influence coefficient method which is an vibration analysis algorithm based on the transfer of influence coefficient is applied to the free vibration analysis of double cylindrical shells. After the computational programs for the free vibration analysis of double cylindrical shells were made using the transfer influence coefficient method and the transfer matrix method, we compared the results using the transfer influence coefficient method with those by the transfer matrix method. The transfer influence coefficient method provided the good computational results in the free vibration analysis of double cylindrical shells. In particular, The results of the transfer influence coefficient method are superior to those of the transfer matrix method when the stiffness of internal springs connecting a inside cylindrical shell and a outside cylindrical shell is very large.

### A Study on the Application of Frontal Transfer Matrix Method to the Beam and the Torsional System (보 및 비틀림계에 대한 Frontal 전달매트릭스법의 적용성에 관한 연구)

• 김영식
• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.22 no.2
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• pp.46-52
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• 1986
• The transfer matrix method has been extensively used to analyze the vibration problem. The final stage in this method is to find out solutions which make the frequency determinant zero. However, the frequency determinant includes the exponential terms and it causes instability to calculation and increases error. Recently the frontal transfer matrix method was suggested by Okada to heighten stability and effectivity in calculation. This paper applied the frontal transfer method to both the beam and torsional system, and confirmed stability and effectivity in comparsion with the transfer matrix method and the Holzer method.

### Dynamic interaction analysis of vehicle-bridge system using transfer matrix method

• Xiang, Tianyu;Zhao, Renda
• Structural Engineering and Mechanics
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• v.20 no.1
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• pp.111-121
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• 2005
• The dynamic interaction of vehicle-bridge is studied by using transfer matrix method in this paper. The vehicle model is simplified as a spring-damping-mass system. By adopting the idea of Newmark-${\beta}$ method, the partial differential equation of structure vibration is transformed into a differential equation irrelevant to time. Then, this differential equation is solved by transfer matrix method. The prospective application of this method in real engineering is finally demonstrated by several examples.

### FETM을 이용한 다자유도 회전체 시스템의 진동해석

• 김승현;김영배
• Proceedings of the Korean Society of Precision Engineering Conference
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• pp.818-821
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• 1995
• A MDOF vibration analysis of the rotor is performed using combined modeling of transfer matrix method and finite element method(FETM). The method combines the advantages of both matrix. Each rotor is modelled using transfer matrix method and treated one element or several ones. The finite element method is applied in composing a system matrix and finding roots. The method used in this is more efficient than conventional finite element method in saving calculation time and provides good results in complex MDOF rotor model.

### Dynamic Analysis of Cracked Timoshenko Beams Using the Transfer Matrix Method (전달행렬법을 사용하여 균열이 있는 티모센코 보의 동특성 해석)

• Kim, Jung Ho;Kwak, Jong Hoon;Lee, Jung Woo;Lee, Jung Youn
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.179-186
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• 2016
• This paper presents a numerical method that can evaluate the effect of crack for the in-plane bending vibration of Timoshenko beam. The method is a transfer matrix method that the element transfer matrix is deduced from the element dynamic stiffness matrix. An edge crack is expressed as a rotational spring, and then is formulated as an independent transfer matrix. To demonstrate the accuracy of this theory, the results computed from the present are compared with those obtained from the commercial finite element analysis program. Based on these comparison results, a parametric study is performed to analyze the effects for the size and locations of crack.

### An Analysis of Continuous Beam by Material Non-linear Transfer Matrix Method (재료비선형 전달행렬법에 의한 연속보의 해석)

• Seo, Hyun Su;Kim, Jin Sup;Kwon, Min Ho
• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.1
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• pp.77-84
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• 2011
• This study is to develop nonlinear analysis algorithm for transfer matrix method, which can be applied to continuous beam analysis. Gauss-Lobatto integral rule is adopted and the transfer matrix is derived from stiffness matrix. In the transfer matrix method, the system equation has a constant number of unknowns regardless of number of D.O.F. Therefore, the transfer matrix method has computational efficiencies not only in linear elastic analysis but also in nonlinear analysis. To verify the developed method, the analysis results of several examples are compared with commercial code in moment-curvature, moment-displacement and load-displacement relation.

### Geometrically non-linear dynamic analysis of plates by an improved finite element-transfer matrix method on a microcomputer

• Chen, YuHua
• Structural Engineering and Mechanics
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• v.2 no.4
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• pp.395-402
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• 1994
• An improved finite element-transfer matrix method is applied to the transient analysis of plates with large displacement under various excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix method is changed into the transfer of generally incremental stiffness equations of every section from left to right. Furthermore, in this method, the propagation of round-off errors occurring in recursive multiplications of transfer and point matrices is avoided. The Newmark-${\beta}$ method is employed for time integration and the modified Newton-Raphson method for equilibrium iteration in each time step. An ITNONDL-W program based on this method using the IBM-PC/AT microcomputer is developed. Finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for dynamic large deflection analysis of plates with random boundaries under various excitations.

### Vibration Analysis of the Helical Gear System by Spectral Transfer Matrix (스펙트럴 전달행렬에 의한 헬리컬 기어계의 진동해석)

• Park, Chan-Il
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.774-781
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• 2006
• This paper presents a study on the analytical prediction of vibration transmission from helical gears to the bearing. The proposed method is based on the application of the three dimensional helical gear behaviors and complete description of shaft by the spectral method. Helical gear system used in this paper consists of the driving element, helical gears, shafts, bearings, couplings and load element. In order to describe all translation and rotation motion of helical gears twelve degree of freedom equations of motion by the transmission error excitation are derived. Using these equations, transfer matrix for the helical gear is derived. For the detail behavior of shaft motion, the $12{\times}12$ transfer matrix for the shaft is derived. Transfer matrix for the bearing, coupling, driving element, and load is also derived. Application of the boundary conditions in the assembled transfer matrix produces the forces and displacements in each element of the helical gear system. The effect of the proposed method is shown by numerical example.