Abstract
This paper presents the solution for the title problem. The solution is found using the exact element method, where the dynamic axial stiffness for the rod is found. The natural frequencies for the variable cross-section member are those for which the stiffness is equal zero. These values can be found up to any desired accuracy. This method is goof for any polynomial variation in the cross-sectional area and mass distribution along the member. The results of several examples are compared with results obtained from finite element analysis.
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