Nonsmooth Chebyshev H-infinity optimization of sparse inerter-dashpot absorber networks for broadband plate vibration suppression

This paper develops a mathematical optimization framework for broadband vibration attenuation of a simply supported thin plate using a sparse network of passive inerter-dashpot dynamic absorbers. The four attachment locations are fixed a priori away from nodal lines of the retained low-order modes; the optimizer allocates a total absorber mass limited to 4.2% of the plate mass and constrains tuning frequency to 75–580 Hz, damping ratio to 0.035–0.290, and inertance ratio to 0.05–4.50 over the selected 45–650 Hz numerical band. A modal Kirchhoff–Love model is condensed with frequency-dependent absorber impedances, and a nonsmooth Chebyshev H-infinity epigraph objective is treated by log-sum-exp smoothing, differential-evolution exploration, and projected local polishing. For the ten-mode benchmark, the robust design reduces nominal peak mobility from 91.889 dB to 85.096 dB: its 6.793 dB reduction exceeds modal tuning by 0.468 dB and the uniform-inerter layout by 1.604 dB. Across fifty material-and-damping perturbation scenarios, its 95th-percentile peak is 1.757 dB below modal tuning, indicating a practically relevant upper-tail benefit, although experimental validation remains necessary. Because the tenth retained plate mode is 385.356 Hz, results above that frequency are reported as exploratory pending a 15–20-mode convergence study.