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Research Papers

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

[+] Author and Article Information
Bao Rong1

Institute of Launch Dynamics,Nanjing University of Science and Technology,Nanjing 210094, People’s Republic of China;  Nanchang Military Academy, Nanchang 330103, People’s Republic of Chinarongbao_nust@sina.com

Xiaoting Rui

Institute of Launch Dynamics,  Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of Chinaruixt@163.net

Ling Tao

 Institute of Plasma Physics,Chinese Academy of Sciences (ASIPP), Hefei 230031, People’s Republic of Chinapalytao@ipp.ac.cn

1

Corresponding author.

J. Appl. Mech 79(2), 021005 (Feb 09, 2012) (8 pages) doi:10.1115/1.4005574 History: Received November 06, 2010; Revised October 12, 2011; Posted February 01, 2012; Published February 09, 2012; Online February 09, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Trapeziform plate and its finite element meshing

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Figure 2

The flow chart for algorithm of random eigenvalue problems

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Figure 3

Cantilever beam and its finite element meshing

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Figure 4

Box beam model and its finite element meshing

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Figure 5

Freely-supported rectangular thin plate

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