Directional algorithms for the frequency isolation problem in undamped vibrational systems

A new algorithm is presented to solve the frequency isolation problem for vibrational systems with no damping: given an undamped mass-spring system with resonant eigenvalues, the system must be re-designed, finding some close-by non-resonant system at a reasonable cost. Our approach relies on modifying masses and stiffnesses along directions in parameter space which produce a maximal variation in the resonant eigenvalues, provided the non-resonant ones do not undergo large variations. The algorithm is derived from first principles, implemented, and numerically tested. The numerical experiments show that the new algorithms are considerably faster and more robust than previous algorithms solving the same problem.