Supplementary file 1_Dynamic analysis of a cantilever beam coupled with bistable nonlinear energy sink: application to vibration suppression.docx

The governing equations of the coupled system are derived using the Euler-Bernoulli beam theory and discretized via the Galerkin method. Under harmonic excitation, the complexification-averaging (CX-A) method and multiple scales technique are employed to investigate the slow-flow dynamics, bifurcation behavior, and the energy transfer mechanism of strongly modulated responses (SMRs).

The results demonstrate that the SMR regime, characterized by relaxation oscillations on the slow invariant manifold (SIM), facilitates efficient and irreversible targeted energy transfer (TET) from the cantilever beam to the BNES. The proposed BNES exhibits superior vibration attenuation over a broad frequency range, highlighting its potential for practical engineering applications.</p>