Finite element studies of hand bell modes.

Abstract

Hand bell modes are identified by indices m and n (m, n), where m refers to the number of nodal lines crossing the crown and n refers to the number of circumferential nodal lines. For high m values, depending on the bell size, no n = 0 modes exist. For such large m modes, the n = 1 nodal line is located very close to the mouth of the bell, rather than near the middle of the bell as is the case for (m,1) modes, where for the same value of m, an n = 0 mode exists. These modes are generally labeled as (m, 1*) modes. Finite element studies of mode sections of increasing complexity indicate that only when two curvatures are introduced, conditions are adequate to give rise to (m, 1*) modes. Computer generated images and animations of mode patterns corresponding to increasingly complex geometries will be illustrated.