论文标题
使用现场表示，在非线性谐振器链的不确定性下进行优化
Optimization under Uncertainty of a Chain of Nonlinear Resonators using a Field Representation
论文作者
论文摘要
长期以来，以春季质量系统形式的谐振器的链条表现出有趣的特性，例如带隙。可以利用此类特征来操纵波浪的传播，例如过滤特定频率，并且更一般地减轻了振动和影响。在系统中添加非线性也可以提供进一步的途径来操纵链中波的传播并增强其性能。这项工作建议通过考虑各种设计不确定性（例如，非线性刚度）和不良的不确定性（例如，加载）来最佳设计这样的谐振器链，以稳健的方式减轻振动。随机优化算法是针对由于存在非线性而量身定制的，以解释链反应中的不连续性。此外，使用字段公式来定义沿链的谐振器的性质，并降低优化问题的维度。结果表明，随机优化算法和场表示的组合会导致可靠的设计，而在链上，最佳性质恒定无法实现。
Chains of resonators in the form of spring-mass systems have long been known to exhibiting interesting properties such as band gaps. Such features can be leveraged to manipulate the propagation of waves such as the filtering of specific frequencies and, more generally, mitigate vibrations and impact. Adding nonlinearities to the system can also provide further avenues to manipulate the propagation of waves in the chain and enhance its performance. This work proposes to optimally design such a chain of resonators to mitigate vibrations in a robust manner by accounting for various sources of design uncertainties (e.g., nonlinear stiffness) and aleatory uncertainties (e.g., loading). The stochastic optimization algorithm is tailored to account for discontinuities in the chain response due to the presence of nonlinearities. In addition, a field formulation is used to define the properties of the resonators along the chain and reduce the dimensionality of the optimization problem. It is shown that the combination of the stochastic optimization algorithm and the field representation leads to robust designs that could not be achieved with optimal properties constant over the chain.
