基于绞制梁结构的非线性减振建模、分析和优化

Nonlinear vibration reduction is superior at conditions of multi-source excitation, complex structure response and broadband vibration reduction requirements. Wire rope based structure is an effective way to achieve nonlinear passive vibration reduction. However, current research fails to take full use of its advantages of broadband and high-efficiency. This project proposes a novel vibration reduction system with the nonlinear characteristics of high-order stiffness and hysteretic damping, which is based on a wire rope structure with both ends constrained. The mathematical model of the system is established with semi-physical method, which describes the nonlinear characteristics such as hysteresis, stiffness varying and pinching effect. The amplitude-frequency response of the vibration reduction system is solved by approximate analytical and numerical methods, which presents the variation of natural frequency and equivalent damping. The stability and bifurcation response of the system are analyzed. The vibration transmissibility is calculated, and the influence of system parameters on vibration reduction performance is revealed. Furthermore, this project proposes a parameter optimization method for nonlinear vibration reduction system based on given requirements. The prototype for wire rope based vibration reduction is developed, based on which, experiments and parameter identification are performed. The proposed mathematical model is modified based on measured characteristic curves. The accuracy of dynamic analysis and the effectiveness of parameter optimization method are verified by vibration reduction experiment. This project aims at providing theoretical basis and technical methods for the development and application of wire rope based vibration reduction equipment.

非线性减振在多源激励、复杂结构响应和宽频减振需求等场景下优势显著，绞制梁结构是实现非线性被动减振的一种有效手段，现有研究成果尚未充分发挥其宽频、高效减振优势。本项目基于两端约束绞制梁结构，提出具有高阶非线性刚度和滞回非线性阻尼特征的新型减振系统。采用半物理方法建立减振系统数学模型，描述滞回、刚度渐变、紧箍效应等非线性特征。利用近似解析和数值方法求解系统幅频响应，研究固有频率和等效阻尼变化规律，分析系统稳定性和分岔响应，计算振动传递率，揭示系统参数对减振性能的影响，提出基于给定减振要求的非线性减振系统参数优化方法。研制减振器样机并开展实验和参数辨识研究，通过特征曲线测量实验改进减振系统数学模型，通过模拟减振实验验证动力学分析的准确性和参数优化方法的有效性。本项目旨在为基于绞制梁结构的减振器研发和应用奠定理论基础，提供技术储备。

减振装置广泛用于航空航天、机械工程和交通运输等领域，同时具有刚度非线性和阻尼非线性的减振装置是实现宽频、高效减振的有效途径，这类双非线性减振系统具有多样的非线性机理、复杂的动力学响应和敏感的结构参数，其动力学建模、分析和优化极具挑战性。本项目针对以绞制梁结构为代表的双非线性减振系统，提出了基于梁约束模型和改进Bouc-Wen模型的物理-唯像混合建模方法，发展了基于恢复阻尼力响应面的唯像建模方法，解决了几何非线性、摩擦非线性和材料非线性的综合表征问题。提出了结合谐波平衡法、时域/频域转换技术、迭代算法和Floquet理论的解析-数值联合分析方法，解决了同时包含高阶多项式函数和隐式微分函数的动力学方程求解问题，提出了广义等效刚度和广义等效阻尼比，分析了包含高阶刚度和滞回阻尼的减振系统的幅频响应、稳定性和参数变化规律，并揭示了惯性加速度对减振系统的动力学影响。提出了基于全局稳定幅频响应的非线性减振系统参数优化方法，实现了最大高静态低动态刚度行程、最小动刚度/静刚度比等目标下的参数优化，对比分析了刚性和柔性非线性减振元件对减振性能的影响，完成了柔性结构-绞制梁减振器和柔性仿生减振器的优化设计。研制了镍钛诺绞制梁减振器和弹簧钢/镍钛诺圆环减振器，利用电子伺服疲劳试验机开展了非线性恢复阻尼力测量实验，利用电磁激振器开展了减振性能测试，验证了减振系统的非线性特征和建模、分析方法的有效性。项目解决了含高阶刚度和滞回阻尼的非线性减振系统动力学分析，以及非线性减振系统的全局参数优化这两项关键科学问题，发展了刚度和阻尼双非线性减振系统的建模、分析和优化设计方法，验证了其宽频、高效减振性能，为其工程应用奠定了理论基础。