Design synthesis of multistable equilibrium systems

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King, Carey Wayne

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Mechanical systems are often desired to have features that can adapt to changing environments. Ideally these systems have a minimum number of parts and consume as little power as possible. Unfortunately many adaptable systems either have a large number of heavy parts and/or continuous actuation of smart materials to provide the adaptive capabilities. For systems where both adaptability and power conservation are desired characteristics, adaptability can be limited by power consumption. Multistable equilibrium (MSE) systems aim to provide a type of adaptable system that can have multiple mechanical configurations, or states, that require no power to maintain each stable configuration. Power is only needed to move among the stable states, and a level of adaptability is maintained. The stable equilibrium configurations are defined by a system potential energy being at a minimum. The design of a MSE system is based around locally shaping a potential energy curve about desired equilibrium configurations, both stable and unstable, such that the basic design goals of position, linearized natural frequency, and transition energy can be specified for the MSE system. By mapping the performance space from the design space in tandem with stochastic numerical optimization methods, the designer determines if a certain system topology can be designed as a MSE system. Qualitative and quantitative mapping procedures enable the designer to decide whether or not the desired design lies near the center or periphery of a performance space. The performance space is defined by the desired design criteria (i.e. locations of the equilibria, natural frequency at the equilibria, etc.) that the designer deems important. If the desired design lies near the periphery of the performance space, a series of optimization trials is performed. This series shows the tendency of the problem to be solved as the desired MSE system characteristics are varied within the performance space from a location where the solution is known to exist to the true desired location where the solution is not guaranteed to exist. Upon analysis of the resulting optimization trends, the designer is able to determine whether or not a feasible limit in the system performance has been reached.