Mathematical modelling of a beam using finite element method

The main purpose of this study was to develop the general mass and stiffness matrices for standard beam equation and eventually obtain the finite element equations for mbira reed. So far few studies have been done on mathematical modelling of a beam using finite elements, with applications to an mbira reed. However none of these studies had considered the aspect of a tapering mbira reed. Thus, the study also intends to examine the relationships that exist between the natural frequencies and the varying dimensions and properties of the mbira reed. The finite element method was used as a numerical method to solve the mathematical model of the mbira reed. A MATLAB code was prepared for the same. The usefulness of this study is that -mbira manufacturers may use the results to select the type and dimensions of metal suitable for mbira reeds. -the outcomes add more knowledge to the existing literature on mbira. -modellers may develop interest to conduct more studies on mbira. - it is useful to engineers who mostly use finite element method in designing and development of different products.