热环境中具有轴向速度扰动的旋转功能梯度薄壁柱壳复杂动力学行为

Rotating shells have been widely used in various fields as core parts. Many rotating shells often serve in thermal environment, where functionally graded materials (FGMs) have a bright application prospect. However, there are very few reports available on investigating the dynamics of rotating FGM shells so far. Meanwhile, environment disturbance have an important impact on vibration of structures, while the influence of velocity disturbance on the vibration of FGM shells have not been paid attention. In view of these situations, this project intends to carry out the research on dynamics of rotating FGM circular cylindrical thin shells with disturbance of axial velocity in thermal environment. By considering the combination of rotation, disturbance of axial velocity and temperature, the dynamical model of rotating FGM cylindrical thin shells will be established. The traveling-mode vibration of rotating FGM cylindrical shells will be studied, and the vibration modes and frequency characteristics of forward and backward waves will be analyzed. By means of nonlinear dynamical methods, the mode interaction and phenomenon of energy exchange in the vibration of rotating FGM cylindrical thin shells will be investigated, the dynamical bifurcation characteristics of system against the disturbance excitation will be analyzed, and the formational process and evolution of attractors in vibration of system will be revealed. The influence mechanism of rotation, disturbance and temperature on the dynamical behaviors of system will also be discussed. The research achievements of this project will gain a deeper insight into the vibration characteristics of rotating FGM shells, and provide theoretical supports for the design of rotating FGM shells.

旋转壳体作为核心构件被广泛应用于诸多工程领域。很多旋转壳体常服役于热环境中，功能梯度材料（FGM）在此领域具有很好的应用前景。然而目前针对热环境中旋转FGM壳体的动力学研究少有报道。同时环境扰动对结构的振动具有重要影响，但在FGM壳体振动研究中速度扰动的影响还没有得到关注。因此本项目拟开展热环境中具有轴向速度扰动的旋转FGM薄壁圆柱壳的动力学研究。综合考虑转速、轴向速度扰动和温度的作用，建立旋转FGM薄壁柱壳的动力学模型。研究旋转FGM柱壳的行波振动，分析其前行波和后行波的振动模态及频率特性。借助非线性动力学方法研究旋转FGM柱壳振动过程中的模态相互作用和能量交换现象，分析系统在扰动激励下的动力学分岔特性，揭示系统振动中吸引子的形成过程及演化规律。讨论转速、扰动和稳态温度对系统各种动力学行为的影响机理。项目研究成果将加深对旋转FGM壳体振动特性的认识，为旋转FGM壳体设计提供理论支持。

本项目主要研究绕轴向旋转和轴向惯性扰动所引起的功能梯度薄壁圆柱壳的动力学行为，同时讨论了热环境对其振动特性的影响。总体上完成了项目的研究计划。主要成果包括：考虑功能梯度材料特性的温度相关性，基于Love薄壳理论，利用Hamilton原理建立了热环境中同时考虑轴向旋转和轴向扰动作用的功能梯度柱壳的动力学模型；采用假设模态法，借助Galerkin法得到了系统广义模态坐标的离散动力学控制方程；基于所建功能梯度薄壁柱壳模型，主要采用多尺度法讨论了系统在周期脉动转速作用下的参数振动稳定性；进一步分析了旋转功能梯度柱壳在轴向扰动作用下的参激响应稳定性，得到了系统在组合参数共振下的不稳定参数域（主要由失稳边界条件和稳定图给出），讨论了轴向扰动幅值、旋转角速度、轴向载荷以及温度、梯度指数及边界条件等对失稳边界的影响。在项目实施过程中，将研究对象扩展到了功能梯度平板和细长梁。初步研究了功能梯度矩形薄板在面内惯性扰动作用下的参数振动稳定性和复杂动力学行为，对其失稳临界条件、阻尼效应以及非线性特性的影响进行了较详细讨论。同时还分析了绕轴向旋转的细长柔性梁在脉动转速和轴向扰动力作用下的动力学特性。需要指出的是：针对功能梯度柱壳在变转速和轴向惯性扰动下的非线性参数振动特性尚需更进一步研究，分析非线性特性对其动力学行为的影响，讨论能量在振动模态间的传递及对参数失稳的影响。

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