Multi-mode vibration suppression of a cantilever beam carrying unbalance rotor using bi-stable nonlinear energy sink

Unbalance in rotating machines, caused by manufacturing defects and wear, can induce severe vibrations in base structures. As the rotor accelerates from static to high speeds, multiple frequencies may be excited. To effectively suppress vibrations across all speeds, a bi-stable nonlinear energy sink (BNES) is attached to a cantilever beam with an unbalanced rotor. The dynamic equation of the beam-BNES system is derived using Euler-Bernoulli beam theory and the Euler-Lagrange equation, followed by Galerkin discretization. A Multi-Objective Genetic Algorithm optimizes the BNES parameters. Results indicate that the BNES reduces multiple resonant amplitudes by 80% to 95%. Energy dissipation for the first and second beam modes was 85% and 78%, respectively. The system’s bifurcation diagram reveals a stable multi-periodic response across a wide range of unbalance levels. Performance measures show that the NES with an additional linear stiffness element or the BNES surpasses traditional NES.