Abstract
The design and optimization of ultrasonic horns require employing accurate models providing a correct representation of the system vibrational modes, and in particular, of the vibrational behaviour at the excitation frequency. Ideally, ultrasonic horns should be designed to vibrate in a purely longitudinal mode at the excitation frequency. For the design to be effective, the actual natural frequency and mode shape of the aforementioned longitudinal mode should be accurately predicted by the dynamic model. In general, simplified models making use of lumped or mono-dimensional elements do not allow representing correctly such a response. On the contrary, complete finite element (FE) models can be very accurate, but they are often too cumbersome to be useful after the design stage. At the optimization stage they usually lead on the one hand to numerical ill-conditioning or unfeasible computational efforts in solving the equations imposed by structural modification algorithms, and on the other to complicate experimental identification of model parameters. The aim of this paper is therefore to propose a novel and general method for model reduction through Craig-Bampton method, in order to synthesize accurate reduced order models providing reliable descriptions of the horn dominant vibrational mode. In particular, the still open problem of the selection of the fixed interface normal modes is discussed. The advantage of the proposed method in term of minimum dimension of the reduced model with respect to the other techniques is demonstrated with reference to a single slot horn, typically employed in ultrasonic welding.