A finite element approach towards understanding violin structural modes.

Abstract

A COMSOL finite element package has been used to model the structural modes of vibration of the violin treated as a shell structure with orthotropic arched plates. Such computations enable the physical properties of the plates, ribs, and soundpost to be varied over many orders of magnitude. This provides major insight into the nature of the coupling of the top and back plates by the ribs and the role of the soundpost in coupling the radiating “breathing” modes of the violin to the weakly radiating anti-symmetric modes excited by the bowed string induced rocking of the bridge on the central island area. Examples will be shown of the influence of such factors as plate thickness/density, anisotropy, arching, rib strength, and position of soundpost on the frequencies and excited strengths of the strongly radiating “signature” modes below 1 kHz. In addition to determining the mode shapes and frequencies of the excited modes, their contributions to the radiated sound are also computed. Comaparison will be made with experimentally observed mode shapes and frequencies.