基于非理想惯容的非线性随机振动抑制

Tuned mass damper is widely applied to structural vibration suppression and has been sufficiently studied. “Inerter” is created by analogy between mechanical and electrical system and can be regarded as the extension of the traditional mass. By introducing inerter to TMD, inerter-based damper can be constructed. By compared with TMD, it is more efficient in vibration suppression and overcomes the mass limitation of TMD. Most existing work is limited to linear system subject to deterministic excitation and the inerter is assumed to be ideal. The present project investigates the random vibration suppression of nonlinear system with non-ideal inerter from the general viewpoint. As a mechanical mechanism, the inherent properties of non-smoothness and uncertainty of inerter are strictly described. The semi-analytical and analytical solutions for the random response of nonlinear structure with typical inerter-based dampers are established. Based on the random response, the process of structural optimization is proposed for different types of objective functions and the proper configuration of the inerter-based damper, the optimal locations and the optimal designed parameters are determined, as well as the performance of vibration suppression. Finally, experiment is given to demonstrate the results. This research can be directly applied to random vibration suppression of engineering structure and in theory the technologies for dealing with the non-smooth factors of stochastic system are developed and mechanism of dual uncertainty of structure and excitation is revealed.

调谐质量阻尼器(TMD)在结构振动抑制中广为采用，且得以充分研究。通过机电类比创造出的“惯容”可视为传统质量概念的推广，将惯容引入TMD构建了惯容式阻尼器，较之TMD，具更好的抑振效果且突破了TMD的质量限制。已有研究多局限于确定性激励的线性系统，且将惯容视为完全理想机构。本项目以一般性观点处理基于非理想惯容的非线性系统随机振动抑制问题。严格刻画作为机械机构的惯容的内在非光滑性和不确定性，建立具有各典型类惯容式阻尼器的非线性结构随机响应解析/半解析预测技术；据此发展针对各类目标函数的结构优化方法，确立惯容式阻尼器的合理构成形式、最优布置位置、最优设计参数及相应的抑振性能；最终，通过实验证实之。本项目的研究可直接应用于工程结构的随机振动抑制，并在理论上发展随机系统非光滑因素的处理技术，揭示系统和激励双重不确定性的作用机制。

相比于经典动力吸振器，惯容式动力吸振器表现出更优异的振动抑制性能，并同时保持着被动特性。“惯容”概念是传统质量概念的推广，通过线惯性和转动惯性转换，由小质量提供大惯性。所谓惯容式动力吸振器，即引入惯容元件形成的新型动力吸振器。本项目以包含惯容式动力吸振器的结构系统为研究对象，研究其随机动力学行为。具体工作包括：以连续梁结构为例，针对不同构型的惯容式动力吸振器，建立其随机振动响应分析方法，讨论惯容元件对结构随机振动响应的影响并以均方随机响应最小为目标优化惯容式动力吸振器的参数；通过周期排布惯容式动力吸振器构建新型弹性超材料，理论预测了其卓越的带隙特性；考虑到作为机构的惯容元件不可避免的非理想因素譬如摩擦和间隙，在一般意义上研究了摩擦和间隙动力学系统的随机振动近似分析方法，并由之讨论了非理想因素对惯容式动力吸振器抑振性能的影响。研究结果表明：惯容式动力吸振器能有效地抑制随机振动响应，并从带宽和低频两方面显著提高弹性超材料的带隙特性。本项目的研究工作拓展了惯容元件在动力吸振领域的应用，相关的非光滑随机动力学分析技术具有普遍适用性。