Normal modes of a circular drum head under nonuniform applied tension: Mode splitting with respect to perturbation symmetry.

Abstract

The effect of nonuniform tension on the normal modes of single headed musical drums is examined. Using the common (m,n) designation, ideal circular membrane modes with m>0 are doubly degenerate. This degeneracy may be lifted by a perturbation to the circular symmetry. Of practical interest to drummers are perturbations caused by nonuniform tension applied at the rim of the drum in the tuning process, leading in some cases to audible frequency splitting. The symmetry of the perturbation determines which of the various two‐fold degenerate modes will split, and to what degree the two resulting frequencies will differ. A selection rule taken from group theory is used, along with principles of perturbation theory, to describe a general model of the frequency splitting of drum modes under the influence of nonuniform applied tension. This model is compared with results of finite element modeling of the membrane normal modes. Experimental results obtained using electronic speckle pattern interferometry (ESPI) are...