The Effects of Damping Rings on Vibration Reduction of 3D Beam Structures

This study investigates the nonlinear vibration of three-stage 3D beams under external forces, with a focusing on internal resonance phenomena arising from geometric variations. By adjusting length and diameter ratios, a 1:3 internal resonance is induced. The analysis primarily examines transverse and lateral coupling effects. The method of multiple scales (MOMS) addresses nonlinear dynamics, utilizing fixed-point plots to assess amplitude and frequency responses under various external forces. Numerical methods are utilized to validate theoretical predictions. Two damping rings are added to the beam to improve vibration damping. Their impact on the main system's vibration damping is analyzed to mitigate internal resonance and optimize vibration reduction. The findings are summarized using a three-dimensional maximum amplitude contour map. Experimental results and theoretical validation confirm the optimal damping effect achieved with the installed damping rings on the three-stage beam model under free boundary conditions.