Physical modeling of the lips in a player/trombone simulation

Simulation of the player/trombone system can provide understanding of its important mechanisms. The player's lips are the most subtle and complex structures of the system. This model of the lip reed introduces the finite element method to represent a continuum structure. Previous lip models used masses and springs, with imposed eigenfrequencies and definite degrees of freedom. In the spirit of physical modeling, the geometry, boundary conditions and material parameters of this continuum model are specified from measurements of the actual system when possible. Presumably, fidelity of the resulting lip modes and lip behavior in simulation reflects the degree of validity of the assumptions made in creating the model.; This work establishes the feasibility of a continuum model of the lips in a simulation of the player/trombone system. The lowest modes of the lip structure recall the swinging and stretching motions of the current theory of the lip reed. These modes can be tuned using boundary conditions and material properties to enable self-sustained oscillation in simulation. Two standard tones are simulated here, as well as a pedal tone. Both the B♭ 2 and F3 utilize a swinging lip mode, showing the lower lip entrained to move with the upper. The motion and waveforms can be compared with those of other models and real players; limited agreement is shown. The main differences are an extended closure phase of the waveform cycle and dissimilarity in the trajectories of a point on the tip of the upper lip. The shape of the area waveform (when open) is encouraging, and radiated pressure waveforms audibly resemble trombone tones. The profound ability to control or tune the embouchure of this model can initiate a new tool of investigation into the mechanisms of player control of the lip reed.