Optimal undercuts for the tuning of percussive beams

Abstract

The paper investigates the use of optimization techniques for the design of percussive beams. Profiles were generated to satisfy predetermined overtone tunings and specified optimization criteria. It is shown that there is no unique solution to the problem, and that the generated profiles need not be the same as traditionally used profiles. The vibration of the beams was modeled using a thick beam theory to take into account the possible effects of shear deformation on the natural frequencies. A number of beams were manufactured with the generated profiles, and their frequency characteristics were obtained experimentally. The experimental results confirm the validity of the numerically generated profiles.