Hand-bell Mode StudiesUwe J. Hansen; Thomas D. Rossing
Handbell modes are generally identified by two indices (m,n). The first one counts the number of nodal lines crossing the crown, while the second one counts the number of circumferential nodal lines. It is notable, that for values of m>3 (depending on bell size) the n=0 modes are missing, instead, an additional set of n=1 modes appears, for which the circumferential nodal line is located very near the mouth of the bell rather than as normally, approximately midway between the crown and the mouth of the bell. These modes which have frequencies above the (m,1) modes are labeled as (m,1*) modes. In an effort to understand the influence of geometry on mode shapes, Finite Element studies with increasingly complex geometry were undertaken. It was discovered that the imposition of overlapping positive and negative curvatures is essential for the formation of the (m,1*) modes.