Change in the dynamic properties of a column as a result of a variable distribution of bending stiffness – numerical and experimental research

The subject of the work is the transverse vibrations of a bar system with a variable cross-section subjected to the follower force directed towards a pole. The issue was formulated on the basis of Bernoulli-Euler’s theory. The solution of the equations of motion substituted for the boundary conditions made it possible to develop a computational algorithm for the frequency of vibrations of the system, taking into account variable stiffness, assuming a constant total volume. On the basis of the obtained results, the relationship between the column stiffness distribution and the eigenvalues of the system was determined. The correctness of the obtained results was verified for selected column outlines, indicating the sources of discrepancies. It was shown that by appropriate shaping of the bar it is possible to control its dynamic properties.