• Title/Summary/Keyword: Transfer matrix method

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

  • Feyzollahzadeh, Mahdi;Bamdad, Mahdi
    • 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.

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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.

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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    • 1995.10a
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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.

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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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    • 2006.05a
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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.

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An Analysis of Hemisphere-cylindrical Shell Structure by Transfer Matrix Method (전달행렬법에 의한 반구 원통형 쉘구조의 해석)

  • 김용희;이윤영
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.45 no.4
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    • pp.115-125
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    • 2003
  • Shell structures are widely used in a variety of engineering application, and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winkler foundation, other problems. In this study many simplified methods (analogy of beam on elastic foudation, finite element method and transfer matrix method) are applied to analyze a hemisphere-cylindrical shell structures on elastic foundation. And the transfer matrix method is extensively used for the structural analysis because of its merit in the theoretical backgroud and applicability. Therefore, this paper presents the analysis of hemisphere-cylindrical shell structure base on the transfer matrix method. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with finite element method.

Prediction of the Sound Absorption Coefficient for Multiple Perforated-Plate Sound Absorbing System by Transfer Matrix Method (전달행렬법에 의한 다중 다공판 흡음시스템의 흡음계수 예측)

  • 허성춘;이동훈;권영필
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.11b
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    • pp.653-658
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    • 2001
  • In this study, a new practical method of predicting the sound absorption coefficient for multiple perforated-plate sound absorbing system was developed using transfer matrix method. In order to validate the proposed method, the absorption coefficients calculated by transfer matrix method for single perforated plate were first compared with the absorption coefficients measured by SWR method according to different porosity, hole diameter, and thickness of the perforated plate. Based on the comparison results, transfer matrix method was further applied to double and triple perforated plates to evaluate the absorption coefficients. The experimental results showed that the absorption coefficients from transfer matrix method generally agreed well with the corresponding absorption coefficients from SWR method. However, due to the limitations of the impedance model used in this study, the measured values were differed with the calculated values for small porosity, hole diameter, and thickness in size of the perforated plate indicating the need of impedance model development for multiple perforated-plate sound absorbing system covering wide ranges of porosity, hole diameter, and thickness of the perforated plate.

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