非线性振动系统中的能量靶向转移分析及调控

Energy targeted transfer is an adjustably one-way transmission of energy. Energy targeted transfer provides a new view point for some engineering problems such as the design of vibration reduction device. Approximate analysis, numerical simulations, and experimental validations will be performed via nonlinear oscillation theory, nonlinear dynamics, and vibration experiment techniques. The resonance conditions required by energy targeted transfer will be clarified, and the effects of nonlinearity will be examined. An index based on the statistics will be worked out to describe quantitatively the energy transferred, and it will be used to investigate the effect of periodical motion, quasi-periodical motion and chaotic motion on the energy transfer. Sensitivity analysis will be carried to locate key parameters, and these parameters will be design to enhance energy targeted transfer. Vibration experiments will be done by use of the shaking table with 3 direction excitations, and analytical and numerical results will be validated. The investigation will establish the conditions of energy targeted transfer in nonlinear oscillation systems, develop approximate analytical methods with numerical confirmations, validate theoretical results, and predict the changing trends of energy targeted transfer with system parameters. The project outcome will enrich the approximate analytical approaches for vibrating systems with strong nonlinearities, understand interaction mechanisms within a nonlinear oscillation system from the view point of energy, and promote the growth of the field of dynamics and control; meanwhile the outcomes will lay the theoretical foundation of designing and optimizing vibration reduction systems.

能量靶向转移是指能量以可调控的方式单向传递。能量靶向转移为研究减振设计等工程问题提供了新的视角。本项目综合运用非线性振动理论、非线性动力学和测试技术，进行近似解析分析、数值仿真和实验验证。明确能量靶向转移的所需要的共振关系及其非线性的影响。定义统计指标定量描述时变转移能量，分析周期运动、准周期运动和混沌运动对能量转移的影响。基于参数敏感性分析确定关键参数，设计这些参数以加强能量靶向转移。在三向激励振动台上进行实验，验证解析分析和数值仿真结果。通过本项目的研究，建立非线性振动系统中能量靶向转移的条件，发展多自由度非线性振动系统的近似分析方法并进行数值验证，用实验验证理论结果，明确能量靶向转移随系统参数的变化趋势。研究成果将发展强非线性振动理论的近似分析方法，从能量观点深入认识非线性振动系统中各子系统相互作用机理，推动动力学与控制学科的发展；同时为设计和优化减振系统奠定理论基础和提供技术储备。

能量靶向转移是指能量以可调控的方式单向传递。能量靶向转移为航天工程减振，提供了新的途径，提高设计水平。本项目综合运用了非线性振动理论、非线性动力学理论和测试技术，通过近似解析分析、数值仿真和实验验证，理解了能量靶向转移现象，并发展了相应被动和主动调控的方法。通过本项目的研究，明确了能量靶向转移所需要的频率关系，发展了多自由度非线性振动系统的近似分析方法并进行数值验证和实验验证，明确了能量靶向转移随相关参数包括补系统参数的变化趋势。研究成果将发展强非线性振动理论的近似分析方法，从能量观点深入认识非线性振动系统中不同子系统相互作用机理，推动了动力学与控制学科的发展；同时为设计和优化减振系统奠定理论基础和提供了技术储备。