Abstract Flutter is a dynamic aeroelastic instability driven by the interaction of inertial, elastic, and aerodynamic forces. It is an undesirable phenomenon in aircraft because it causes divergent oscillations that may lead to structural damage or failure, performance and ride comfort degradation, or loss of control. If flutter is discovered at the aircraft certification stage, costly redesign is required. Performing flutter analysis early in the design process can mitigate this problem. Furthermore, including flutter analysis as a constraint in multidisciplinary design optimization reduces the risk of costly modifications late in the design cycle. We review the methods for flutter analysis in the context of aircraft design optimization. We also include methods for predicting post-flutter limit cycle oscillations due to the increasing impact of nonlinear effects on future aircraft. While there has been extensive work in flutter and post-flutter analyses, developing design optimization constraints associated with these analyses has additional requirements, such as acceptable computational cost, function smoothness, robustness, and derivative computation. We discuss these requirements and review efforts in the development, implementation, and application of flutter and post-flutter constraints in aircraft design optimization. We conclude the paper by summarizing the current state of this field and the main open problems. Flutter constraints have been included in structural optimizations, but optimizing both the structural sizing and the aerodynamic shape remains a challenge due to the need to recompute the aerodynamic properties at each design iteration. Additional difficulties arise in the presence of large structural deflections and transonic flow conditions due to the dependency of the flutter point on the equilibrium state and the high cost of nonlinear computations. Post-flutter constraints have rarely been included into design optimization, but they are crucial in the prevention of undesirable limit cycle oscillations. Implementing such constraints requires the development of more efficient and robust prediction methods that can handle realistic configurations. While this paper focuses on flutter and post-flutter constraints for aircraft design optimization applications, the considerations and challenges are broadly applicable to the optimization of engineering systems including stability and post-critical dynamic constraints.

中文翻译：

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飞机设计优化中的颤振和颤振后约束

摘要 颤振是一种由惯性力、弹性力和气动力相互作用驱动的动态气动弹性失稳。这是飞机中不受欢迎的现象，因为它会导致发散振荡，从而可能导致结构损坏或故障、性能和乘坐舒适性下降或失去控制。如果在飞机认证阶段发现颤振，则需要进行昂贵的重新设计。在设计过程的早期执行颤振分析可以缓解这个问题。此外，将颤振分析作为多学科设计优化中的约束可降低设计周期后期成本高昂的修改风险。我们回顾了飞机设计优化背景下的颤振分析方法。由于非线性效应对未来飞机的影响越来越大，我们还包括预测颤振后极限循环振荡的方法。虽然在颤振和颤振后分析方面有大量工作，但开发与这些分析相关的设计优化约束有额外的要求，例如可接受的计算成本、函数平滑性、鲁棒性和导数计算。我们讨论了这些要求，并回顾了飞机设计优化中颤振和颤振后约束的开发、实施和应用。我们通过总结该领域的现状和主要未解决的问题来总结本文。颤振约束已包含在结构优化中，但由于需要在每次设计迭代时重新计算空气动力学特性，因此优化结构尺寸和空气动力学形状仍然是一个挑战。由于颤振点对平衡状态的依赖性和非线性计算的高成本，在存在大的结构偏转和跨音速流动条件时会出现额外的困难。后颤振约束很少包含在设计优化中，但它们对于防止不希望的极限循环振荡至关重要。实施此类约束需要开发可以处理现实配置的更有效和更强大的预测方法。虽然本文侧重于飞机设计优化应用的颤振和颤振后约束，