The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the system’s responses are highly sensitive to uncertainty and can even exhibit a discontinuous behavior. This represents a major hurdle for the optimization, which is already hampered by the potentially large computational cost associated with the time integrations. To tackle the high-sensitivity to uncertainties and reduce the computational burden, a dedicated surrogate-based stochastic optimization algorithm is used. Specifically, the approach uses Kriging surrogates built from the unsupervised identification of clusters resulting from response discontinuities. Comparisons between efficiencies of optimal nonlinear absorbers with and without time-dependent stiffness are performed and discussed.

中文翻译：

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具有瞬态三次非线性的目标能量转移的随机优化


考虑具有随时间变化的刚度的非线性能量汇 (NES) 的随机优化。 NES 线性耦合到主系统。优化的目的是找到 NES 的刚度特性，使主系统速度的预期值最小化，同时考虑激励幅度和频率的统计分布。结果表明，系统的响应对不确定性高度敏感，甚至可能表现出不连续的行为。这代表了优化的一个主要障碍，而与时间积分相关的潜在巨大计算成本已经阻碍了优化。为了解决对不确定性的高敏感性并减少计算负担，使用了专用的基于代理的随机优化算法。具体来说，该方法使用克里金代理，该代理是根据响应不连续性产生的集群的无监督识别而构建的。对具有和不具有随时间变化的刚度的最佳非线性吸收器的效率进行了比较并进行了讨论。