The transfer matrix method seen as one method of structural analysis among others

Uhrig, Richard

doi:10.1016/0022-460x(66)90117-9

Cited by 37 publications

(17 citation statements)

References 8 publications

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“…If we combine equation (29) with equation (25), the buckling mode can be obtained. In order to demonstrate the method, two typical examples are considered: a C-section member and a Z-section member.…”

Section: Illustrations Of Open Cross-section Membersmentioning

confidence: 99%

“…28 The classical transfer matrix method (TMM) has been developed as an effective tool for structural analysis, especially for chain connected system from topological perspective. 29 By combining the TMM and FEM, the finite element-transfer matrix method (FE-TMM) is developed to analyze the static and dynamic of structural problems. 30 And then a structural analysis method, named as boundary element-transfer matrix method (BE-TMM), is proposed for the vibration analysis of two-dimensional plate acted by uniform 31 and concentrated 32 loads.…”

Section: Introductionmentioning

confidence: 99%

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Buckling analysis of thin-walled members via semi-analytical finite strip transfer matrix method

Zhang

Yao

et al. 2016

Advances in Mechanical Engineering

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Slender thin-walled members are main components of modern engineering structures, whose buckling behavior has been studied widely. In this article, thin-walled members with simply supported loaded edges can be discretized in the cross-section by semi-analytical finite strip technology. Then, the control equations of the strip elements will be rewritten as the transfer equations by transfer matrix method. This new method, named as semi-analytical finite strip transfer matrix method, expands the advantages of semi-analytical finite strip method and transfer matrix method. This method requires no global stiffness matrix, reduces the size of matrix, and improves the computational efficiency. Compared with finite element method's results of three different cross-sections under axial force, the method is proved to be reliable and effective.

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Section: Illustrations Of Open Cross-section Membersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling analysis of thin-walled members via semi-analytical finite strip transfer matrix method

Zhang

Yao

et al. 2016

Advances in Mechanical Engineering

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“…Compared to the transfer matrix, the finite element method has the advantage of accurately modeling rotor bearing systems with a fewer number of elements while being less sensitive to numerical instabilities, although sometimes it requires more CPU time and computer storage (Ruhl and Booker, 1972). On the other hand, with the transfer matrix approach, as problem size increases, numerical difficulties arise (Uhrig, 1966 (1963,1965), Ruhl and Booker (1972) used cubic hermitian-shape functions to formulate the shaft element matrices, including only the elastic bending energy and kientic energy. Using the Rayleigh beam theory, Nelson and McVaugh (1976) generalized the work of Ruhl and Booker by the addition of other factors, such as rotatry inertia, gyroscopic moments, and axial load.…”

Section: Rotating Shaft Finite Element Modelmentioning

confidence: 99%

Finite Element Modeling of a Rotor Shaft Rolling Bearings System With Consideration of Bearing Nonlinearities

El-Saeidy¹

1998

Journal of Vibration and Control

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“…1 Compared with other matrix methods of structural analysis, such as the displacement method and the force method, TMM uses both displacements and internal forces at nodal points of the structure. 2 Later, many improvements and applications of TMM have been found from a science research and engineering technology point of view. For science research, the Riccati transformation can be regarded as an important tool to improve numerical stability of transfer computation.…”

Section: Introductionmentioning

confidence: 99%

Differential quadrature discrete time transfer matrix method for vibration mechanics

Xue

Wang

2019

Advances in Mechanical Engineering

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Transfer matrix method is a practical technology for vibration analysis of engineering mechanics. In this article, a new version of mixed differential quadrature discrete time transfer matrix method is presented for simulating vibrations. First, ordinary differential equations of the substructure or the element of a mechanical system are determined by classical mechanics rules or the finite element method. These ordinary differential equations can be transformed to a set of algebraic equations at some discrete time points by the application of a differential quadrature method. After extending the state vector of the transfer matrix method, new transfer equations and transfer matrices of the substructures (or elements) of a mechanical system are developed finally. Riccati transformation is used to improve the computational convergence of the method. Several numerical examples show that the proposed method can be regarded as an efficient tool for transient response analysis of vibration systems.

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The transfer matrix method seen as one method of structural analysis among others

Cited by 37 publications

References 8 publications

Buckling analysis of thin-walled members via semi-analytical finite strip transfer matrix method

Buckling analysis of thin-walled members via semi-analytical finite strip transfer matrix method

Finite Element Modeling of a Rotor Shaft Rolling Bearings System With Consideration of Bearing Nonlinearities

Differential quadrature discrete time transfer matrix method for vibration mechanics

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