转动薄壁圆柱壳行波振动的非线性特性研究

In steam turbine engines, advanced gas turbines, aircraft jet engines and other rotating machinery, many components utilize thin-walled cylindrical shells. Mechanical faults, such as fatigue damage and rub-impact, induced by the vibration of cylindrical shell, are the core problems affecting the reliable operation of rotating machinery. Different from generic stationary shells, vibrations of rotating thin cylindrical shells are in the form of travelling wave, thus their dynamic behaviors are more complicated. Starting from the dynamic practical problem of thin cylindrical shells in rotating machinery, the nonlinear characteristics of the traveling wave vibration of thin cylindrical shells are studied based on nonlinear dynamic theory: 1) Taking into account geometric nonlinearity as well as gyroscopic effect due to rotating, the nonlinear dynamic model of a thin rotating cylindrical shell is derived and a novel model reduction strategy is proposed to downscale the degrees of freedom; 2) Based on the reduced model, principal resonance and stability, as well as internal resonance mechanism and characteristics, are investigated by using harmonic balance method combined with arc length continuation technique.The results will reveal the nonlinear dynamic evolution of the traveling wave vibration of thin rotating cylindrical shells, and provide technical reserve for the design or analysis of thin cylindrical shells in rotating machinery. Moreover, the present work may show us a viable path to perform theoretical study on infinite dimensional gyro system with nonlinearity.

在蒸汽轮机、燃气轮机、航空发动机等旋转机械中，有许多部件采用薄壁圆柱壳作为其主要结构形式。圆柱壳型薄壁构件振动导致的疲劳破坏、碰摩等故障，是影响旋转机械可靠运行的核心问题之一。有别于传统的静止壳，转动薄壁圆柱壳的振动具有行波振动的典型特点，其动力学行为更为复杂。本项目从旋转机械中圆柱壳型薄壁构件的动力学实际问题出发，基于非线性动力学理论，开展转动薄壁圆柱壳行波振动的非线性特性研究：1)考虑几何非线性，以及转动产生的陀螺效应，建立转动薄壁圆柱壳行波振动的非线性动力学模型，并提出一种模型简化降阶策略，得到适合非线性动力学分析的低阶模型；2)基于该低阶模型，采用谐波平衡法结合弧长延拓技术研究行波振动的主共振与稳定性，以及内共振机理与特性。研究结果将揭示转动薄壁圆柱壳行波振动的非线性动力学演化规律，为旋转机械中圆柱壳型薄壁构件的设计或分析提供技术储备，同时为无限维非线性陀螺系统的理论研究提供思路。

本项目从旋转机械中圆柱壳型薄壁构件的动力学实际问题出发，基于非线性动力学理论，开展转动薄壁圆柱壳行波振动的非线性特性研究，主要研究内容和结果如下：1）转动薄壁圆柱壳行波振动的非线性动力学建模：建立了转动薄壁圆柱壳行波振动的非线性动力学模型，并提出了一种模型简化降阶策略，得到适合非线性动力学分析的低阶模型；2）转动薄壁圆柱壳行波振动的主共振及稳定性研究：揭示了壳体随转速变化非线性动力学行为演化规律，研究发现随着转速从零开始增加，主共振幅频曲线逐步脱离出两个共振峰，分别对应（伪）驱动模态和（伪）伴随模态，且转速越高，共振峰越趋离；3）转动薄壁圆柱壳行波振动的耦合内共振机理及特性研究：几何尺寸巧合和转速巧合是两种触发1:1:1:1内共振的机制，其中，由转速巧合引起的内共振是转动薄壁圆柱壳特有的一种内共振行为。本项目研究成果可为旋转机械中圆柱壳型薄壁构件的设计或分析提供理论依据。