Inverse mode problems for the finite element model of a vibrating rod |
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Authors: | Xia Tian |
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Institution: | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China |
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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. |
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Keywords: | Eigenvalue Inverse problem Rod Finite element model |
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