Review of nonlinear modal analysis in friction damping structures of blades/blade disks
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摘要:
概述了非线性模态的理论基础以及非线性动力学分析的一般数值方法；进而针对含干摩擦非线性环节的结构，总结了阻尼非线性模态的相关研究进展；在此基础上，重点综述了国内外近十年来采用阻尼非线性模态数值方法在航空发动机带冠叶片、缘板阻尼器、叶根阻尼与干摩擦阻尼环分析与设计中的应用；列举了目前用于验证非线性模态的先进试验技术。提出了非线性模态在干摩擦阻尼结构动力学分析中亟需解决和关注的若干问题。研究表明：非线性模态逐渐从理论研究阶段过渡到工程应用阶段。结合模型降维技术，阻尼非线性模态已经可用于提取带干摩擦阻尼叶片/叶盘高保真有限元模型的模态特征。拓展能量平衡法与非线性模态综合法搭建了非线性模态与稳态响应的桥梁，可以显著提升基于响应的参数分析效率。非线性模态试验技术的研究处于起步阶段，尚无法应用于工程复杂结构。
Abstract:The definitions of the nonlinear modes and the numerical methods to solve a nonlinear dynamic problem were reviewed. The progress in application of the damped nonlinear normal modes for structures with frictional damping was summarized. The related researches in the last decade for different friction damping devices were also summarized, including the tip shrouded blades, underplatform dampers, blade root damping and friction ring dampers. Furthermore, test works related to nonlinear modal testing were also reviewed. Open problems and future directions were highlighted. It was concluded that the nonlinear mode gradually developed from the theoretical stage to engineering stage. Combined with ad-hoc reduced order modeling techniques, nonlinear modal analyses were implemented to reveal the modal characteristics of high-fidelity finite element models of frictionally damped blades/blisks. The extended energy balance method and nonlinear modal synthesis were employed to build a bridge between nonlinear modes and steady-state response, which can significantly improve the efficiency of response-based parameter analysis. Nonlinear modal testing still in its infancy cannot be applied to engineering structures yet.
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Key words:
- nonlinear vibration /
- damped nonlinear normal mode /
- dry friction damper /
- blade /
- blade disks
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图 1 杜芬振子系统以周期运动描述的非线性模态
Figure 1. Nonlinear mode for Duffing oscillator in periodic motion description
图 2 杜芬振子系统以不变流形描述的非线性模态
Figure 2. Nonlinear mode for Duffing oscillator in invariant manifold description
图 3 2自由度高次刚度非线性系统的内共振
Figure 3. Internal resonance of the 2 degrees of freedom nonlinear system with higher-order stiffness
图 10 宏滑移摩擦模型（詹金斯单元）与微滑移摩擦模型（Dahl）迟滞回线对比
Figure 10. Hysteresis loops of the macroslip friction model （Jenkins element） and microslip friction model （Dahl）
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