Repeated Wave-Shock Mitigation on High-Speed Boats by Nonlinear Modeling and Optimization of a Suspension Seat

Abstract

It is known that high-speed craft crews are subjected to repeated vertical shock during wave slamming, and that such exposure is related to lumbar spine injury and with poor operational performance. Most previous seat-design studies have modeled the hull as a single moving base and ignored pitch coupling, which can be interpreted as a seat located at the center of gravity of the vessel and thus unable to simulate its pitch-induced excitation at any other station. In this work a ten DOF (23-state) nonlinear model is introduced that includes a rigid hull free in heave and pitch, a passive seat with four simultaneous nonlinearities (polytropic air spring, asymmetric quadratic damper, Bouc–Wen hysteretic friction element, and progressive end-stop), and a seven-segment ISO 5982 biodynamic occupant. The two-station bow/stern slamming formulation, with a fore/aft encounter phase lag, represents the physical origin of the heave–pitch coupling, which is the wave loading. The daily equivalent static compression dose is calculated from seat-pan acceleration that is filtered through the ISO 2631-5 lumbar filter. The governing equations are stiff and are close to non-smooth and therefore they are integrated using an implicit solver and each nonlinear element is checked against its analytical limit one by one. Then, suspension parameters and seat longitudinal offset are optimized using a particle-swarm procedure under four objective formulations: an exposure limit feasibility objective referenced to Directive 2002/44/EC, a balanced six-metric scalarization, a peak head-acceleration objective and a daily spinal dose objective. Mapping the daily spinal dose onto the speed–sea-state operating plane, the optimized seat enlarges the area of that plane lying below the ISO 2631-5 low-risk criterion by 66.0% and the area lying below the high-risk criterion by 66.3%. The analysis also reveals a band of resonant operating speeds, centered near 9.3 m·s−1, within which a decrease in craft speed paradoxically increases the risk to the occupants. No single formulation dominates: each scalar single-objective optimum attains the best value of its own criterion, the formulations separating weakly in occupant dose but by a factor of 3.5 in suspension travel. Re-evaluated on an unseen sea state the dose-driven optimum degrades by 163% in spinal dose and exceeds the vibration dose value exposure limit by a factor of 2.4, because it consumes 132 of the 150 mm of available travel, whereas the balanced design retains 112 mm of reserve and is unaffected; stroke reserve, rather than in-sample dose, is what carries performance across sea states. The analysis further shows that an under-stroked seat can transmit a narrow acceleration peak exceeding the peak at its own base: the baseline seat reaches a peak transmission ratio of 2.06, whereas all four optimized designs hold this ratio at or below 0.61, with implications for seat specification and mission planning. All quantitative outcomes reported here are model-based predictions, conditional on the stated parameter set, and await experimental validation.