A violin shell model: vibrational modes and acoustics.

A generic physical model for the vibro-acoustic modes of the violin is described treating the body shell as a shallow, thin-walled, guitar-shaped, box structure with doubly arched top and back plates. comsol finite element, shell structure, software is used to identify and understand the vibrational modes of a simply modeled violin. This identifies the relationship between the freely supported plate modes when coupled together by the ribs and the modes of the assembled body shell. Such coupling results in a relatively small number of eigenmodes or component shell modes, of which a single volume-changing breathing mode is shown to be responsible for almost all the sound radiated in the monopole signature mode regime below ∼1 kHz for the violin, whether directly or by excitation of the Helmholtz f-hole resonance. The computations describe the influence on such modes of material properties, arching, plate thickness, elastic anisotropy, f-holes cut into the top plate, the bass-bar, coupling to internal air modes, the rigid neck-fingerboard assembly, and, most importantly, the soundpost. Because the shell modes are largely determined by the symmetry of the guitar-shaped body, the model is applicable to all instruments of the violin family.