Predicting the vibratory response of bladed-disks in turbomachinery is of the utmost importance to design a reliable and optimized engine. Yet, such simulations are challenging mainly due to the large size of the finite-element model used to describe the system, the existence of random mistuning created by manufacture tolerances, and the nonlinear effects arising from the different components and their coupling. As a consequence, very few reduced-order models handling nonlinear mistuned systems have yet been proposed and the existing ones try to find the best compromise between a computationally efficient simulation and a correct description of the nonlinear phenomena. In this paper, a novel approach is proposed to tackle this challenge. Its key ideas rely on the substructuring concept and the cyclic properties of the structure. A reduction basis composed of cyclic complex nonlinear normal modes is created on each sector of the system leading to a compact nonlinear superelement per sector. The system is then assembled and a synthesis simulation is performed. Due to the main concepts employed, the method is referred to as the Substructuring method based on Nonlinear Cyclic Reduction (SNCR). It is validated on a finite element model of a tuned, a randomly mistuned and an intentionally mistuned bladed-disks. It will be shown to be fast and accurate despite strong nonlinearities. Due to its flexibility and efficiency, the method is expected to have a wide range of possible applications within the community.

预测涡轮机械中的叶片盘的振动响应对于设计可靠且优化的发动机至关重要。但是，由于用于描述系统的有限元模型的尺寸较大，存在制造公差所造成的随机失谐以及不同组件及其耦合产生的非线性影响，因此这种模拟具有挑战性。结果，很少有人提出处理非线性迷惑系统的降阶模型，现有模型试图在计算效率高的仿真与对非线性现象的正确描述之间找到最佳折衷方案。在本文中，提出了一种新颖的方法来应对这一挑战。它的关键思想依赖于子结构概念和结构的循环特性。在系统的每个扇区上创建由循环复数非线性法线模式组成的约简基础，从而导致每个扇区紧凑的非线性超元素。然后组装系统并执行综合仿真。由于采用的主要概念，该方法称为基于非线性循环归约（SNCR）的子结构化方法。它在已调谐，随机错位和有意错位的刀片磁盘的有限元模型上得到了验证。尽管存在很强的非线性，它将被证明是快速而准确的。由于其灵活性和效率，该方法有望在社区中广泛应用。然后组装系统并执行综合仿真。由于采用的主要概念，该方法称为基于非线性循环归约（SNCR）的子结构化方法。它在已调谐，随机错位和有意错位的刀片磁盘的有限元模型上得到了验证。尽管存在强烈的非线性，它将被证明是快速而准确的。由于其灵活性和效率，该方法有望在社区中广泛应用。然后组装系统并执行综合仿真。由于采用的主要概念，该方法称为基于非线性循环归约（SNCR）的子结构化方法。它在已调谐，随机错位和有意错位的刀片磁盘的有限元模型上得到了验证。尽管存在强烈的非线性，它将被证明是快速而准确的。由于其灵活性和效率，该方法有望在社区中广泛应用。尽管存在强烈的非线性，它将被证明是快速而准确的。由于其灵活性和效率，该方法有望在社区中广泛应用。尽管存在强烈的非线性，它将被证明是快速而准确的。由于其灵活性和效率，该方法有望在社区中广泛应用。