On the dynamic characteristics of using track nonlinear energy sinks for structural vibration control

Nonlinear energy sinks (NESs) have emerged as a promising solution to overcome the narrow effective bandwidth of linear dynamic vibration absorbers such as the tuned mass damper (TMD). In particular, track NESs are increasingly attracting attention as they are capable of generating nonlinear restoring forces by the movement of an additional mass on the curved tracks. The present study aims to investigate and explore the versatile characteristics of track NESs in structural vibration control. To this end, three different track profiles are considered, namely the profiles designed by a quartic term only, by combined positive quadratic and quartic terms, and by combined negative quadratic and positive quartic terms. Their profiles and damping coefficients are analytically derived in closed form. The frequency response functions of standalone track NESs are constructed using the Harmonic Balance Method and compared with those obtained by the 4th-order Runge-Kutta method, and the dynamic responses, including the displacements, the phase planes, the nonlinear stiffness forces, and the vibrational frequencies, of the track NESs are presented and discussed under different excitation amplitudes and frequencies. The effectiveness and robustness of using track NESs for structural vibration control are also systematically investigated and compared with TMD under harmonic and white-noise ground excitations. Results show that the closed-form solutions of optimal profile and damping coefficients are sufficiently accurate for lightly damped structures, and the frequency response functions of track NESs can be accurately estimated using the Harmonic Balance Method for low and moderate excitations, although their dynamic responses are sensitive to the excitation amplitudes and frequencies. Furthermore, in comparison to TMD, the track NESs are superior in terms of decreased stiffness and smaller working strokes. In general, the present study demonstrates the potential of using track NESs as an effective and robust alternative for structural vibration control.