项目名称： 多自由度非线性系统的振动能量传递机理及应用

项目编号： No.11472057

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 张君华

作者单位： 北京信息科技大学

项目金额： 86万元

中文摘要： 多自由度非线性系统能够描述很多工程实际问题，如广泛应用于航空航天等领域的蜂窝结构，这类系统的振动问题备受关注。本项目拟研究工程问题中复杂激励作用下多自由度非线性系统模态间的能量传递机理及蜂窝夹层板的非线性动力学行为。主要内容包括：发展多脉冲Melnikov无穷积分计算方法，给出复杂系统出现多脉冲混沌的参数域，揭示模态振动与能量传递之间的关系。计算多自由度非线性系统模态振动的相位，研究系统模态共振与模态间相位同步的关系，进一步明确模态之间能量传递的机理。考虑气动力-温度场及复杂机械载荷联合作用下，建立蜂窝夹层板的非线性动力学模型。研究蜂窝夹层板的多脉冲能量传递、模态间的相位同步、运动稳定性及分叉等非线性动力学行为。本项目旨在丰富非线性动力学理论，推动非线性动力学理论的发展及其在实际工程中的应用；为蜂窝结构在航空航天领域应用的优化设计和振动控制提供理论指导和技术支持。

中文关键词： 振动能量传递；多脉冲混沌；相位同步；蜂窝夹层板；多场耦合

英文摘要： Multi-degree-of-freedom nonlinear system can describe many practical engineering problems, such as honeycomb structure which is used widely in aerospace and other fields and the vibration of such systems was highly concerned. The project intends to study energy transfer between models of the multi-degree-of -freedom nonlinear system under complex excitations from engineering problems and the nonlinear dynamics of honeycomb sandwich plates. The main contents include: Develop multi-pulse Melnikov infinite integral calculated method, give domains of parameters of the complex nonlinear system when the system has multi-pulse chaos and reveal the relationship between the modal vibration and energy transfer. Calculate the phases for multi-degree-of-freedom nonlinear system modal vibration and study the relationship between modal resonances of systems and the phase synchronization between models which can further clarify the mechanism of energy transfer between modes. Consider aerodynamic-temperature loads and complex mechanical loads and establish the dynamic model of honeycomb sandwich plates. Research the energy transfer between multi-pulse bumps of the honeycomb sandwich plates, the phase synchronization between modes, other nonlinear dynamics such as stability and bifurcations. The project aims is to enrich the theory of nonlinear dynamics, to promote the development of nonlinear dynamics theory and its application in practical engineering; provide theoretical guidance and technical support to optimize the design and vibration control for honeycomb structure more widely used in aerospace applications.

英文关键词： Vibrational energy transfer;multi-pulse chaos;phase synchronization;honeycomb sandwich plate;multi-field coupling