基于波型转换和能量局域效应的Moebius结构隔振机理研究

The Moebius strip structure is a naturally twisted and curved plate/shell structure. The wave mode conversion mechanism and energy localization phenomena of the Moebius strip structure are investigated from the aspect of dynamics. A new type of isolation structure is proposed accordingly. For theoretical aspects, the wave propagation characteristics of the naturally twisted plate/shell are studied first; then the free vibration problem and the forced responses of the Moebius strip structure are investigated, and the distribution of the energy carried by different waves is analyzed to reveal the wave mode conversion mechanism and energy localization phenomena; in addition, the first-order shear theory is developed to study the energy dissipation mechanism for naturally twisted structure coated with unconstrained layer damping. For experimental aspects, the modal shapes, as well as the distribution of the bending, tension and twist deformation energy are measured to verify the energy localization mechanism; the input/output properties and the vibration transmission of the Moebius isolation structure are tested to validate the wave mode conversion mechanism and the isolation performance. The findings will deepen insight into the wave mode conversion mechanism and energy dissipation mechanism of naturally twisted structures and lay a solid theoretical foundation for the design.

Moebius带状结构是一种具有初始扭曲和弯曲的板、壳结构，项目从动力学的角度揭示其波型转换机理和能量局域效应，并据此构造一种新型隔振结构。在理论方面，从初始扭曲板、壳结构的波传播特性出发，研究Moebius带状结构的自由振动特性和强迫响应特性，分析其中各种波携带的能量及其空间分布，揭示其波型转换机理和能量局域效应；并采用一阶剪切变形理论分析初始扭曲板、壳结构和Moebius带状结构在表面粘贴自由阻尼层时的能量耗散机制。在实验方面，测试Moebius带状结构的模态振型以及弯曲、拉伸和扭转应变能的分布，验证其能量局域效应；测试Moebius隔振结构的输入输出导纳特性和隔振系统中的振动传递特性,验证其波型转换机理和隔振性能。研究成果将有助于加深对初始扭曲结构波型转换机理和能量耗散机制的理解，为此类隔振结构的设计提供坚实的理论依据。

本项目从理论分析和试验研究两个角度揭示了Moebius结构隔振器的波型转换和能量局域隔振机理、非线性刚度机理。在理论上，建立了初始扭曲板结构、粘贴和不粘贴自由阻尼层Moebius结构的数值模型，获得了其模态特性、在不同类型激励力作用下的力传递特性和能量传递特性，明确了此类结构的模态局域效应和能量局域效应、波型转换特性。在试验上，研制了粘贴和不粘贴自由阻尼层Moebius结构样机，并由多个Moebius结构构建了Moebius隔振器，通过LDV（激光多普勒测速仪）测试了此类形状复杂薄壁结构的频响函数、模态特性；通过Moebius隔振器静压试验、基础激励下的传递特性试验、Moebius隔振器单自由度隔振系统的传递特性试验获得了Moebius隔振器的高静刚度低动刚度刚度特性、高阻尼特性。这些特性是微观隔振机理在宏观性能上的表现。这两方面的研究表明，Moebius隔振结构和隔振器具有优良的性能，体现在：（1）Moebius结构和隔振器具有理想的高静刚度低动刚度刚度特性（准零刚度特性）；（2）Moebius结构和隔振器的阻尼性能很好，模态阻尼比能够达到0.046（粘贴自由阻尼层的金属结构的模态阻尼比通常为0.01左右）；（3）Moebius隔振器的原点阻抗大，跨点导纳在整个频段内的衰减大。因此，所提出的Moebius隔振结构和隔振器具有较好的工程应用价值。