Idealized models of reed woodwinds. Part II : on the stability of two-steps oscillations
Sébastien Ollivier, Jean Kergomard, Jean-Pierre Dalmont · INRIA a CCSD electronic archive server · 2004
The stability of "two-step" oscillations in cylindrical and conical-like reed woodwinds is investigated within the scope of Raman's model applied to woodwinds. The use of idealized resonators which can be characterized by two reflection functions leads to iterative equations, from which a criterion for the stability of the oscillations can be derived by using a perturbation method. This criterion depends on the waveform and on the shape of the nonlinear pressure/flow characteristics. It is consistent with similar criteria given by previous authors for the bowed string and for the clarinet. Stability of some waveforms is firstly investigated for any characteristics, then for given elementary models of single reed woodwinds and results are compared to time domain simulations.