Analytical and Experimental Investigation of the Rotary Inertia Effects of Unequal End Masses on Transverse Vibration of Beams

In this study, the transverse vibration of free-free slender beams with two unequal end masses attached were studied. The effects of the rotary inertia of the end masses on the free vibration of the beam were investigated. An exact frequency equation and the boundary conditions were obtained by using the Euler-Bernoulli beam theory and Hamilton's principle. Natural frequencies and mode shapes of the beams in transverse vibrations were calculated for various combinations of physical and geometrical parameters, such as mass ratios, the distances between the attachment point and the center of the masses, etc. The effects of an increase in the rotational inertia of the end masses and different mass ratios on the natural frequencies and mode shapes of the beam are presented. It is shown that the increase in the rotational inertia of the end masses had a greater effect at low frequencies of the beam. In addition, experimental tests were performed to validate the obtained analytical results. A good agreement was obtained between the analytical and experimental results. The main scope of this study was to reveal the effects of the rotary inertia of the end masses on the dynamic behavior of the beam. Thus, the aim is to contribute to the understanding of the properties of the end mass and the effect of rotary inertia on the dynamics of end-mass-attached structures. Furthermore, the results obtained from this research are helpful for designing end-mass-attached structures, such as micromechanical sensors, energy harvesters, and Stockbridge-type dynamic absorbers.