Influence of the Variability of the Shape of Short Axisymmetric Rods on the Value of Basic Natural Frequency of Longitudinal Vibrations

Rods with a relatively short length in relation to their transverse dimensions with a variable cross-section along the axis, subjected to longitudinal vibrations, have the character of stocky rods, for which the classic geometric principles used for rods are not fully met. For small engineering elements, the postulated design frequencies of natural vibrations in the very high cycle fatigue analyses reach the values of a dozen or so, small, several dozen kHz. In the article, the sensitivity of the value of the basic natural frequency to the change in the shape of the element is analysed and discussed. The analysis is conducted using finite element method.