Abstract
This paper proposes a method by which calculation of the natural frequencies of bending vibration of a straight rod accompanied by an additional mass and subjected to axial compression, and the estimation the axial force based on the natural frequency are made easy. This method is an extension of Rayleigh's method. The effect of the additional mass on the mode shapes is first studied using a rigorous analysis. The deflections of the rod assumed in the calculation are modified principal mode shapes of bending vibration of a rod with neither additional mass nor axial force. Comparisons between calculated results and experimental results show that if the additional mass is lighter than about half of the mass of the rod, natural frequencies up to the third mode are obtained with good accuracy, and that estimation of the axial force is made with errors of less than ten percent.
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