Mode selection for reduced order modeling of mechanical systems excited at resonance

Welding, food cutting, atomizing, cleaning and deagglomerating are just a few common uses for ultrasonic resonators, which are carefully designed to operate excited in resonance. Finite element analysis is nearly always adopted for predicting and improving resonator performances. Large number of small elements are usually needed to guarantee accuracy. As a consequence, models have typically very large dimensions, and hence considerable computational and ill conditioning problems arise. Model reduction techniques can be extremely useful to keep model dimensions to a minimum. In this paper a new ranking method, called Interior Mode Ranking (IMR), is introduced for the selection of the interior normal modes in the Craig Bampton reduction technique, which is one of the most popular model reduction methods, often available in commercial finite element software packages. The IMR method allows ranking the interior modes analytically by comparing the contributions provided by the interior modes of the subsystem with constrained boundary conditions to the dynamics of interest of the complete system (with actual boundary conditions). The method is general and can be applied to any resonator in the reduction at the system level. Here it is employed to obtain an accurate reduced-order model of an ultrasonic welding bar horn. The results achieved by the method are compared with those yielded by other ranking techniques. The comparison shows that the IMR method outperforms the other ranking techniques and leads to accurate representations of the excited modes.