The major goal of this paper is to address the derivation of the frequency equation of flexural vibrating cantilever beam considering the bending moment generated by an additional mass at the free end of beam, not just the shear force. It is a transcendental equation with two unambiguous physical meaning parameters. And the influence of the two parameters on the characteristics of frequency and shape mode was made. The results show that the inertial moment of the mass has the significant effect on the natural frequency and the shape mode. And it is more reasonable using this frequency equation to analyze vibration and measure modulus.
Wang, B., Wang, Z., & Zuo, X. (2017). Frequency Equation of Flexural Vibrating Cantilever Beam Considering the Rotary Inertial Moment of an Attached Mass. Mathematical Problems in Engineering, 2017. https://doi.org/10.1155/2017/1568019