Numerical and experimental modal analysis of the reed and pipe of a clarinet

Abstract

A modal computation of a complete clarinet is presented by the association of finite-element models of the reed and of part of the pipe with a lumped-element model of the rest of the pipe. In the first part, we compare modal computations of the reed and the air inside the mouthpiece and barrel with measurements performed by holographic interferometry. In the second part, the complete clarinet is modeled by adjoining a series of lumped elements for the remaining part of the pipe. The parameters of the lumped-resonator model are determined from acoustic impedance measurements. Computed eigenmodes of the whole system show that modal patterns of the reed differ significantly whether it is alone or coupled to air. Some modes exhibit mostly reed motion and a small contribution of the acoustic pressure inside the pipe. Resonance frequencies measured on a clarinet with the mouthpiece replaced by the cylinder of equal volume differ significantly from the computed eigenfrequencies of the clarinet taking the actual shape of the mouthpiece into account and from those including the (linear) dynamics of the reed. This suggests revisiting the customary quality index based on the alignment of the peaks of the input acoustical impedance curve.

Study of vibration and sound characteristics of a copper gong

“…Through the validated finite element model, the adjustment of violin modal properties can be numerically predicted and fitted to desired resonance peaks. Facchinetti et al (2003) applied finite element analysis (FEA) and experimental mode analysis (EMA) to study the vibration behaviors of reed and pipe in a clarinet. The holographic interferometer was used to observe the vibration modes and eigenfrequencies of the reed.…”

Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches

“…As before (Section D.3), we set f actor n,0 = 1. The array of reconstructed resonance frequencies r n,s,m can be computed by multiple regression using an array of matrices W s,m,k : r[n, s] = W [s] · f actor[n] (20) As before (Section D.4), we have also the option to reduce the dimensionality from K toǨ, using the previously defined array of matricesM [s] and then use a unique matrixŴ m,ǩ to operate the multiple regression: r[n, s] =Ŵ ·M [s] · f actor[n] (21) We call these 2 options: hypotheses H10 and H11. For H11, we performed a small orthogonal rotation of the factors to concentrate the information about the hygrometric material properties in f actor n,4 , for a better fit.…”

“…Different authors (among them Casadonte [18,19], Facchinetti et al [20,21] and Guimezanes [17]) modeled the clarinet reed by Finite Elements Method (FEM) and computed the first few eigenmodes. They chose appropriated values of the elastic parameters in the literature, ignoring however viscoelastic behavior.…”

Imaging a vibrating object by Sideband Digital Holography

“…Here, we use digital heterodyne holography [9]; both reference and illumination laser beams are frequency shifted, and the selection of one sideband is obtained by a proper detuning of one of the beams followed by heterodyne detection on a CCD camera; this technique provides much more flexibility and leads to accurate quantitative measurements. As a demonstration, inspired by the work described in [10,11] we perform an experiment where the vibrating object is the reed of a clarinet; in addition to the intrinsic interest of such an object, with its possible musical implications, a reed provides a test system that is particularly well adapted to our purposes, with typical vibration amplitudes of the order of 0.1 mm. We will see that, even with smaller amplitudes, there is no difficulty in obtaining holographic images corresponding to the n th sideband with n up to 100 or more.…”