Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Bao Rong ◽  
Xiaoting Rui ◽  
Guoping Wang
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Eigenvalue Problems ◽  
Flexible Structures ◽  
System Matrix ◽  
Element Transfer ◽  
High Computational Efficiency

The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer matrix method and finite element method, the modified finite element-transfer matrix method and its algorithm for eigenvalue problems are presented. By using this method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This method has the low order of system matrix, high computational efficiency, and stability. Formulations of this method, as well as some numerical examples, are given to validate the method.

Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Bao Rong ◽  
Xiaoting Rui ◽  
Ling Tao
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Eigenvalue Problems ◽  
Computational Stability ◽  
Random Eigenvalue ◽  
Uncertain Structures ◽  
Element Transfer ◽  
High Computational Efficiency

The rapid computation of random eigenvalue problems of uncertain structures is the key point in structural dynamics, and it is prerequisite to the efficient dynamic analysis and optimal design of structures. In this paper, by combining finite element-transfer matrix method (FE-TMM) with perturbation method, a new method named as perturbation FE-TMM is presented for random eigenvalue problems of uncertain structures. By using the proposed method, the rapid computation of random eigenvalue problems of uncertain structures with complicated shapes and boundaries can be achieved, and the repeated eignvalues and characteristic vectors can be solved conveniently. Compared with stochastic finite element method, this method has the low memory requirement, high computational efficiency and high computational stability. It has more advantages for dynamic design of uncertain structures. Formulations as well as some numerical examples are given to validate the method.

Discrete Time Finite Element Transfer Matrix Method Development for Modeling and Decentralized Control

2015 ◽  
Author(s):  
Nick Cramer ◽  
Sean Swei ◽  
Kenny Cheung ◽  
M. Teodorescu
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Discrete Time ◽  
Flight Control ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Structural Control ◽  
Method Development ◽  
Time Step ◽  
Element Transfer

The current emphasis on increasing aeronautical efficiency is leading the way to a new class of lighter more flexible airplane materials and structures, which unfortunately can result in aeroelastic instabilities. To effectively control the wings deformation and shape, appropriate modeling is necessary. Wings are often modeled as cantilever beams using finite element analysis. The drawback of this approach is that large aeroelastic models cannot be used for embedded controllers. Therefore, to effectively control wings shape, a simple, stable and fast equivalent predictive model that can capture the physical problem and could be used for in-flight control is required. The current paper proposes a Discrete Time Finite Element Transfer Matrix (DT-FETMM) model beam deformation and use it to design a regulator. The advantage of the proposed approach over existing methods is that the proposed controller could be designed to suppress a larger number of vibration modes within the fidelity of the selected time step. We will extend the discrete time transfer matrix method to finite element models and present the decentralized models and controllers for structural control.

Combined finite element-transfer matrix method based on a mixed formulation

1985 ◽  
Vol 20 (1-3) ◽  
pp. 173-180 ◽  
Author(s):  
Edward E. Degen ◽  
Mark S. Shephard ◽  
Robert G. Loewv
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Mixed Formulation ◽  
Element Transfer
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