An eigenvalue approximation for parameter-dependent undamped gyroscopic systems

Parameter–dependent eigenvalue problem occurs in a host of engineering contexts. Structural design under dynamic loading is concerned with the evaluation of eigenvalues for a large number of structures, each evaluation corresponding to a combination of design parameters. Exact calculation of the natural frequencies of all the models considered is computationally expensive. Here structural problems that possess gyroscopy, typically encountered in the analysis of rotating elastic structures, are considered. Approximate but inexpensive calculations are sought for this class of problems. In the present work, an algorithm for approximating the natural frequencies of undamped gyroscopic systems is presented. Numerical examples show excellent accuracy, while affording significant computational economy compared to exact calculations. The computational gain is found to be relatively more notable when the size of the considered problem is large