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Title: Simulation, Design Selection and Validation of a Negative Stiffness-Based Deck Suspension System for Mitigation of Shock and Vibration in a High-Speed Craft

Authors: David W. Shahan, Richard Akers, Jason Aughenbaugh, Carolyn C. Seepersad, Preston S. Wilson, Michael R. Haberman, D. Dane Quinn, Larry Bergman, Alex Vakakis, Sean Hubbard, D. Michael McFarland, Christopher P. Henry

Abstract: Under Phase 2 of the Defense Advanced Research Projects Agency (DARPA)’s Structural Logic program, HRL with its combined university and commercial team have pushed development of highly robust, high-performance negative-stiffness structures and devices out of the lab and into the challenging, extreme-shock and -vibration environment to help prevent injuries in high-speed planing craft. The design approach centers around an open-loop optimization of performance criteria over a wide set of anticipated sea conditions. First, rigid-body, 30-knot planing motions from a 23’ Specmar Inc. Orca kit boat are simulated in POWERSEA software using a fully developed International Towing Tank Conference (ITTC) spectrum of 30-minute-long seaways across 27 diverse significant wave heights (H1/3 = 0.4-1.2m) and mean modal wave periods (Tmodal = 3.3 -7.5s). Next, input heave acceleration and pitch time histories are applied to a mechanical lumped element model of the boat with a bow-hinged deck and a bilateral arrangement of two negative stiffness-based suspensions in series. The time-domain simulation methodology captures the nonlinearities of the negative stiffness-based suspension, damping and bump stops together with the corresponding relative motions and reaction forces of the hull and deck. These suspension elements are parameterized to easily apply multi-parameter design search and optimization methods (genetic algorithm, Pareto front and gradient) in Matlab and C simulations across the set of anticipated seaways. Design evaluation is based on improvements in program metrics (reductions in daily equivalent static compression dose value for an 8 hour endurance (SED8), lumbar acceleration and frequency weighted root-mean-square (RMS) acceleration) relative to an identical boat ballasted to the same mass, longitudinal center of gravity and radius of gyration. The selection of optimal suspension constitutive behavior with broad seaway robustness will be highlighted. Mechanical and suspension model refinement to achieve experimentally validated performance will be shown using targeted small-scale physical testing to validate models and accelerate manufacturing and design maturity. To improve this modeling approach, we recommend development of a closed-loop time-domain simulation capability to properly capture feedback of nonlinear suspension forces (that prevent launching) and unsprung mass effects (resulting in amplified heave acceleration of the hull) when evaluating reaction forces and motions at the hull-water interface. Design, build and comparative boat test results are highlighted in a companion paper.

The views, opinions and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.