Mathematical modelling of linear elasticity of a three-dimensional block using finite elements: the Case of the Wooden Base of a Mbira

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Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
University of Dar es Salaam,
Abstract
For the first time, the contribution of the wooden base of mbira on overall sound quality of the mbira is being investigated. The main objective of the study was to assess the contribution of the natural frequency of the wooden base on the overall sound quality of the mbira. Numerical and experimental work wan performed to determine the natural frequency of wood using 3D - linear elasticity and finite element method. The structural computations were built on the idea that, wood is an elastic material, although in some references wood possesses a non-linear mechanical behavior. Thus, the natural frequencies of different wooden bases of the mbira (hardwood and softwood) of equal dimensions were accessed using the mathematical model established. The natural frequency of the high note mbira reed was measured and found to be (526 Hz). Furthermore, there was another source of frequency that ranged from 9.0 Hz to 20 Hz which was thought to be the natural frequency of the wooden base of the mbira. However, the natural frequencies of the two types of the wooden bases of the mbira were found to be 540 Hz for softwood and 650 Hz for hardwood. This means that the frequency we were looking for (around 10 — 20Hz) certainly doesn’t come from the motion of the wooden base of the mbira which we had hypothesised. Clearly the natural frequency of the wooden base of a mbira does not contribute anything on the overall sound quality of the mbira and the base might be a first level amplifier or the base act as a sound absorber. To improve or extend this study one may wish to investigate: (i)The best wood for higher amplification of sound of the mbira reeds, (ii)The effect of curvature on the mbira reeds to the overall performance of the mbira.
Description
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF TA420.M523)
Keywords
Wood, Mechanical Property, Finite element method, Linear elasticity
Citation
Mjankwi, M A (2012) Mathematical modelling of linear elasticity of a three-dimensional block using finite elements: the Case of the Wooden Base of a Mbira Master dissertation, University of Dar es Salaam. Dar es Salaam