1. Inverse mode problems for the finite element model of a vibrating rod
- Author
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Tian, Xia and Dai, Hua
- Subjects
- *
INVERSE problems , *NUMERICAL analysis , *FINITE element method , *BARS (Engineering) -- Vibration , *MASS (Physics) , *EIGENVALUES , *EIGENVECTORS , *MATHEMATICAL physics - Abstract
Abstract: The inverse mode problems for the finite element model of an axially vibrating rod are formulated and solved. It is known that for the finite element model, based on linear shape functions, of the rod, the mass and stiffness matrices are both tridiagonal. It is shown that the finite element model of the rod can be constructed from two eigenvalues, their corresponding eigenvectors and the total mass of the rod. The necessary and sufficient conditions for the construction of a physically realizable rod with positive mass and stiffness elements from two eigenpairs and the total mass of the rod are established. If these conditions are satisfied, then the construction of the model is unique. [Copyright &y& Elsevier]
- Published
- 2009
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