Graph models of wind instruments : computing the natural frequencies of some elementary ducts

International audienceA graph-based modelling approach for wind instruments with tone holes has been recently proposed by the author. This preliminary work remained at a rather theoretical level with high degree of generality, focussing nevertheless on musical acoustics applications while laying foundations for concrete applications. The purpose of the present work is to present concrete computation methods and numerical results in order to validate these theoretical results. For this task, elementary resonators are investigated, for which great knowledge has been accumulated for a long time through the impedance, transfer matrix and modal decomposition approaches, which can thus serve for checking. The resonator profiles focussed on belong to a musically useful class : cylinders and stepped cones, as studied by Dalmont and Kergomard 20 years ago. The case of a cylindrical resonator with one tonehole is also presented. One important feature of the approach is that mode matching is automatically satisfied, natural frequencies and eigenmodes being computed at once by the method, even for geometries with discontinuities. Also, perspectives are opened for exhibiting a very wide class of resonators with harmonically related natural frequencies, which is the subject of an another paper

The irish Uillean pipe: a story of lore, hell and hard D

International audienceThe irish Uillean pipe is a bellows-blown bagpipe that resembles other baroque musettes (french musettes de cour) such as the english Northumbrian pipe and french Musette. According to A. Baines, it appeared in Ireland in the late seventeenth century, in a version somewhat simpler than the instrument known in the present days. It is surely among the most evoluated bagpipes nowadays with a rather complex playing. The lowest note of the chanter has the noticeable characteristic, searched after by musicians, of having two different timbres. One of these, known among musicians as the hard D, is strikingly louder and clearer than the other, the soft D. The contrast between them is traditionally a much appreciated quality of an instrument. In this paper, we concentrate on this particular note and propose an explanation for the appearance of these two distinct timbres

Rest to rest motion for planar multi-link flexible manipulators through backward recursion

In this work is considered the problem of rest-to-rest motion in a desired pre-fixed time for planar flexible manipulators. We introduce a simple idea permitting the minimization of end-effector residual vibration when reaching a desired angular equilibrium position, in a pre-fixed desired travelling time. The results hold without considering internal elastic damping effect, using a classical controller with feedforward plus joint feedback terms. The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. This backward integration yields basically elastic trajectories permitting to reach the final desired end-effector position without oscillation. The feedback controller is then used to stabilize locally the actual states along these desired trajectories. However, for fast rest to rest motion, the feedback compensator fails to drive the system states along the desired trajectories, this being due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques, the goal being the minimization of the initial elastic error associated to these joint trajectories. The optimal planning technique is formulated as a Pontryagin optimal control problem. This scheme is validated via numerical tests as well as experiments on a flexible two-link planar manipulator