多振子耦合准零刚度隔振浮筏的非线性隔振和减振机理研究

Controlling vibrations and noises born from onboard machines is vital to the marine hydroacousitc stealth and combat technical performances. The quasi-zero stiffness (QZS) vibration isolation raft coupling with multiple oscillators is proposed to simultaneously prevent oscillations, especially with low-frequency, transmitting to the base and suppress vibrations of raft, which will be new technology and methodology for vibration control of onboard machines. A compact QZS isolator is developed to replace the traditional isolator mounted on the vibration isolation raft, leading to a QZS vibration isolation raft. To realize low-frequency vibration isolation, which cannot be achieved by traditional rafts, the complex nonlinear dynamic characteristics of the raft system will be studied comprehensively, and then the vibration isolation performances will be evaluated under excitations with multiple sources and multiple frequencies. Further, the QZS raft is coupled with several nonlinear oscillators. High dimensional nonlinear dynamic equations of the coupling dynamic system are established. The analytical solution form of response with tiny amplitude is constructed based on numerical simulations. The approximate analytical solutions are achieved by multi-scale method, and then the mechanism of amplitude death will be discovered by analyzing the evolving rule of the amplitude against variations of coupling parameters. The critical values of design variables are obtained by bifurcation analysis, and then the parameter regions for amplitude death are achieved. Therefore, vibration control of raft can be realized when the design variables are selected from the parameter regions of amplitude death (Death island). Finally, the reducing scale experimental prototype of QZS vibration isolation raft is fabricated. Experimental tests are carried out to obtain time histories of system responses, and then force and power flow transmissibility are given based on the test data to evaluate the vibration isolation performances of QZS raft. Meanwhile, the vibration control of raft by coupling multiple nonlinear oscillators is also verified by experimental tests.

机械振动噪声控制对提高舰船声隐身性能和作战技能至关重要。本项目提出多振子耦合准零刚度隔振浮筏方法，隔离（尤其是低频）振动向船体传递，同时控制筏架的振动，以期为舰船机械振动控制提供新的解决途径和方法。将准零刚度隔振器替代现有隔振器，构造准零刚度隔振浮筏，为达到传统浮筏难以实现的低频隔振效果，深入研究多源多频激励下浮筏系统的复杂非线性动力学特性和隔振性能。进一步，准零刚度浮筏耦连非线性振子群，形成多振子耦合系统，建立高维非线性动力学方程，由数值仿真给出微幅响应解的形式，利用多尺度法求得振幅解析解，揭示耦合参数变化导致振幅解演化的规律，即振幅死亡机理，利用分岔分析确定振幅死亡临界条件，给出振幅死亡参数区域（死亡岛），从而实现对浮筏振动的控制。最后，制备多振子耦合准零刚度隔振浮筏的实验装置，基于实测响应计算功率流传递率等指标，评估准零刚度浮筏的隔振性能，验证多振子耦合振动控制方法的有效性。

特种装备中广泛存在的振动问题制约了舰船声隐身等高精尖技术的突破性发展，尤其是低频减振隔振是国内外公认的理论瓶颈和技术难题。针对这一挑战，本课题提出了多振子耦合准零刚度隔振浮筏方法，在准零刚度低频隔振理论与方法、准零刚度隔振器设计与开发、多振子耦合准零刚度超结构设计等方面开展了系统的研究，以期同时隔离低频振动向船体传递和抑制筏架的结构振动，为舰船机械振动提供新的减振隔振方法。主要研究成果包括：（1）发展了准零刚度隔振方法，提出了多种新型准零刚度隔振器和多向隔振平台，并研制了实验样机，验证了准零刚度隔振器的超低频隔振性能；首次探索了制造误差对准零刚度隔振性能的影响，揭示了工程实际中无法实现理想超低频隔振的原因。（2）首次提出了多振子耦合准零刚度局域共振超结构的概念和设计方法，揭示了超结构低频减振的机理，探索了负刚度结构对带隙的调控机制；创新设计了多振子耦合局域共振杆、轴、梁、板等超结构，并研制了实验样机，验证了多振子耦合准零刚度超结构的低频减振性能。（3）研究了多振子耦合局域共振超结构的非线性动力学特性，发现了弹性波在超结构中传播的幅值相关性以及超传输行为，初步阐明了利用非线性调控弹性波的机理。（4）针对超结构低频减振带隙狭窄、减振效果一般的固有缺陷，提出了利用惯性放大机构提高振子的等效质量，进一步降低减振带隙频率，提高减振效果；开发了分布式多频准零刚度振子，实现了多个相邻窄带融合为宽频带隙；提出了电磁主动准零刚度振子，实时对负刚度进行调节以适应激励频率的变化，从而实现减振带隙的实时调控。本课题立足于国家需求，从理论和样机实验的角度证实了多振子耦合准零刚度超结构的低频减振隔振特性，为解决舰船、航天、精密加工、特种医疗器械等领域广泛存在的低频减振隔振难题，提供了新的理论基础和技术途径，研究成果具有良好的技术前瞻性和工程应用前景。