Method for Calculating Natural Frequencies of Bending Vibration of a Stepped Cylindrical Rod Subjected to Axial Compression and Estimation of the Axial Force

This paper proposes a method which facilitates the calculation of natural frequencies of bending vibration of a stepped cylindrical rod subjected to axial compression and the estimation of the axial force. This method is an extension of Rayleigh's method. First, the effects of the position of the step of nonuniform diameter on the mode shapes are discussed using the results of a rigorous analysis. Then, the stepped rod is replaced by a rod of uniform diameter, and the same method is applied. Deflection functions used in this method are modified from the 1st to the 3rd mode shapes of bending vibration of the uniform rod. Finally, the accuracy and limitations of this method are discussed based on the comparison between calculated results and experimental ones.