Eigenstructure assignment in undamped vibrating systems: A convex-constrained modification method based on receptances

摘要

The problem of designing vibrating systems having a desired eigenstructure is addressed in this paper using a method based on receptances. The method proposed relies entirely on receptances and hence neither analytical nor modal models are needed. The problem is formulated as a constrained inverse eigenvalue problem in order to ensure the physical feasibility of the solutions computed. The formulation proposed, suitable for linear undamped systems, allows handling an arbitrary number of assigned eigenpairs and of modifiable parameters. Moreover, a regularization term allows biasing the solution towards preferable modifications and can assure good numerical conditioning. Finally, since the problem is formulated as a convex-constrained problem, a unique solution must exist and can be computed through effective and fast convergence rate algorithms. A numerical example and the comparison with a well-established method demonstrate that the proposed method provides effective results. The application of the method to the modification of a laboratory vibrating system gives experimental evidence of its effectiveness.