Finite element analysis and experimental measurements of natural eigenmodes and random responses of wooden bars used in musical instruments

Finite element analysis was used to study the vibrational properties of wooden bars for musical instruments. Following this numerical method, natural eigenmodes and random responses of constant section and undercut bars were calculated. The vibrational analysis achieved with these results focused on two main points. First, a study of the influence of each elastic parameter of wood on natural eigenfrequencies was carried out using for this material an orthotropic description. Second, the influence of an undercut on the vibrational behaviour of wooden bars was described. Finally, all the results were compared with experimentally obtained measurements. Two main conclusions have been inferred from these results. First, some parameters of wood seem to be the most important for natural eigenfrequencies: the Young modulus and shear moduli along the grain and the density. Second, the achievement of harmonical relationships between frequencies have been studied for different undercut shapes analysing the eigenmode extraction and frequency responses together. Thus, it leads to a direct application to the carving process of xylophone or marimba bars. (C) 1998 Elsevier Science Ltd. All rights reserved.