Type and number of elements effect on the calculation of cantilever beam free natural frequencies using the finite element method

The free vibration calculation of a rectangular cross-section cantilever beam will be analyzed in this study. Using the finite element method (FEM), the stiffness and mass matrices were created and solving the behavior equation with a general program suitable for any number of a one-dimension element using (MATLAB) program. For the same condition, but with different numbers and types of elements, the (ANSYS) software will be used to simulate the cantilever beam. The first three natural frequencies and mode shapes are investigated for each case, and the results compared with the exact solution. The results showed that the difference between the exact and numerical results are decreases when the number of elements increases and the one-dimension element used with the (MATLAB) is more efficient for beam, one-dimension element (BEAM188 & BEAM189) gives more efficient results with less number of elements in comparing with the two and three-dimensions element (PLANE183 & SOLID186), two and three-dimensions element (PLANE182 & SOLID185) needs high number of elements to give suitable results.