Inverse Mode Problems for the Discrete Model of a Vibrating Beam

✍ Scribed by Y.M. Ram

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 326 KB
• Volume: 169
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1016

✦ Synopsis

Discrete models are constructed for a non-uniform cantilever beam by using eigendata. While the classical inverse vibration problem for the vibratory beam determines a model from eigenvalues corresponding to various end conditions, the constructions here are mainly based on eigenvector data. It is shown that, for a given mesh, a finite difference model may be constructed from two eigenvectors, one eigenvalue and the total mass of the beam. If the mesh is unknown, then the model, including the grid points, may be determined from three eigenvectors, one eigenvalue and total mass and length of the beam. The practical situation, where the data are subject to noise, is also considered. To reduce the sensitivity of the model to perturbations an optimal solution, in the least squares sense, is derived by using overdetermined data. The results may be applied to the evaluation of discrete models for the non-uniform beam by using experimental modal analysis data.