【作者】 张力；

【导师】 薛松涛； 谢丽宇；

【作者基本信息】 同济大学 ， 工程（能源与环保）（专业学位）， 2023， 博士

【摘要】 振动现象在工程领域广泛存在且大多数对生产生活有害,在我国工业制造进行技术产业升级以及大规模都市圈同步规划建设的关键阶段,高精度、高质量的设备产品需求大幅增加,同时,工程防灾也面临更加严峻的挑战。基于此,有必要进一步研发高适用性、高性能的减振(震)控制技术。基于非线性手段的非线性减隔振(震)技术已被证明是一种高效的被动振动控制策略,现有非线性技术多是利用刚度或阻尼非线性进行构造,而线性惯容概念的出现为基于此的两端点非线性惯性的构造提供了一种新的思路,即非线性惯容。现有非线性惯容实现方式多是基于几何非线性构造附加线性惯容的间接性实现,增加了附加构造要求,且相关研究多数为概念性装置。鉴于此,本研究利用轭型机制提出了一种非线性惯容的直接实现,称为轭型非线性惯容,并加工了实体样机,开展了相关的动力试验研究以及基于轭型惯容的隔振系统及非线性动力吸振器系列研究。首先,基于轭型机制介绍了轭型非线性惯容的概念,并设计了易于工程实现的轭型惯容构造。基于牛顿定律以及拉氏方程分别建立了轭型惯容的力学本构模型,并进行了轭型惯容的非线性惯性力特征分析,加工了轭型惯容实体样机并进行了动力试验研究,结合多体动力学模型模拟以及动力试验研究结果分别进行了轭型惯容力学模型验证,并分析了装置间隙非线性的影响,定性地总结了相关的影响规律。研究结果表明,所建议的轭型惯容能够有效产生表观质量,且具有非线性的惯性力及非线性的动态负刚度效果,多体动力学模拟及动力试验研究结果均与理论本构模型匹配良好,因而验证了所建立模型的正确性。惯容装置间隙会使得其力学行为曲线产生明显突变现象,且在一个简谐运动周期循环内,会产生两处突变,力突变现象的位置在达到简谐运动最大位移前出现,另外,在固定加载幅值下,加载频率不会影响间隙引起的力突变的位置。在进行精细化性能分析时,建议考虑间隙对惯容装置力学性能的影响。其次,建议附加轭型惯容以提升传统隔振系统的性能,采用平均法求解了轭型惯容隔振系统的骨架曲线及谐波激励下的动力响应解析解,并基于此对其动力学特性及稳定性进行了分析,采用动力响应、传递率、有效隔振频带以及功率流的性能指标,系统性评估了力激励以及基底位移激励下轭型惯容隔振系统的隔振性能,并与传统隔振、线性惯容隔振以及菱形机构非线性惯容隔振系统进行了综合的性能对比。研究结果表明,轭型惯容隔振系统的自振频率与激励幅值相关,且随幅值的增加而减小。谐波激励下轭型惯容隔振系统的幅频响应曲线在相同的激励频率与幅值下出现多解与跳跃现象,需要研究系统稳定性问题。在力激励与基底位移激励下,附加轭型惯容均能够有效抑制隔振系统的传递率峰值,拓宽有效隔振频带。在相同的名义惯质比下,轭型惯容隔振系统具有比传统隔振、线性惯容隔振以及菱形机构非线性惯容隔振系统更强的综合隔振性能,因而能提供一种高效的隔振系统性能提升方案。然后,建议了一种基于轭型惯容的非线性吸振器(YI-NLVA)以实现高性能减振,分析了单独YI-NLVA减振装置的动力特性及性能特征,求解了附加YI-NLVA减振结构的非线性模态,分析了该减振结构的动力学特性,对比相同惯质比下的线性调谐惯容阻尼器(TID)动力学特性,明确了YI-NLVA减振结构的复杂动力学行为。采用基于能量的性能指标,对比线性TID研究了脉冲激励下YI-NLVA减振结构的减振性能。在谐波激励下,采用复变量平均法求解了附加YI-NLVA减振结构的响应解析解,并对比TID减振结构综合分析了系统的减振性能。研究结果表明,YI-NLVA装置自由振动的频率与初始速度的大小相关,且初始速度越高,YI-NLVA自由振动的频率越低。附加YI-NLVA减振结构的同相位与异相位振动频率均随着初始输入能量的增加而减小,且表示其非线性模态的同相位及异相位构形平面图随着能量的增加从近似线性变化为显著的非线性,表现了系统动力学特性及动力行为的复杂性及多样性。在脉冲激励下,对比TID减振结构,YI-NLVA减振结构能在更宽的频带下具备较高的耗能比。在谐波激励下,对比线性TID,YI-NLVA的减振性能鲁棒性更高,且综合减振性能更高效。最后,分别针对随机激励下附加轭型惯容的船舶用设备隔振系统、不同强度地震作用下附加轭型惯容的基础隔震以及附加YI-NLVA的减震结构进行算例分析,并对比了附加具有相同惯质比的线性惯容所对应减隔振(震)结构的性能。研究结果表明,在传统船舶设备隔振系统中附加轭型惯容能够有效地降低位移时程最大值、传递力时程最大值、位移与力传递函数峰值,且对比线性惯容设备隔振系统,轭型惯容设备隔振系统具有更高效的隔振性能。在多遇地震下,采用基于轭型惯容的隔震和减震性能提升方案与采用相同惯质比的线性惯容方案具有几乎相同的效果。但在罕遇地震下,采用基于轭型惯容的隔震和减震性能提升方案均明显优于采用相同惯质比的线性惯容隔震和减震性能提升方案。其中,在罕遇地震下,对于基础隔震结构,附加轭型惯容对比附加对应线性惯容的方案性能平均提升20%;而对于吸振器减震结构,附加YI-NLVA对比附加TID的方案性能平均能够提升17%。综上,基于轭型非线性惯容的减隔振(震)结构均具有较好的工程应用前景。更多还原

【Abstract】 Vibration phenomena are widespread in the engineering field,and most of them are detrimental to production and daily life.In China,during a crucial phase of technological industrial advancement,there is a substantial demand for high-precision,high-quality equipment and products.Simultaneously,in the stage of the synchronous planning and construction of large urban areas,the field of engineering disaster prevention faces increasingly severe challenges.Therefore,it is imperative to further develop vibration control technologies that are characterized by high applicability and performance.Nonlinear vibration suppression techniques that are implemented through nonlinear methods have proven to be efficient passive control strategies.Existing nonlinear techniques predominantly utilize stiffness or damping nonlinearity for their construction.The emergence of linear inerter concept provides a new insight for constructing two-terminal nonlinear inertial elements,which is named as nonlinear inerter.However,current implementations of nonlinear inerter are primarily achieved by incorporating linear inerters into geometrical nonlinear mechanisms,which is an indirect method.This increases the need of supplementary construction components.Moreover,the existing investigations in this area remain largely conceptual.In light of these issues,this study introduces a direct implementation of nonlinear inerter,named as yoke-type nonlinear inerter.The corresponding prototype device is fabricated and the dynamic experimental tests are conducted.A series of investigations on isolation systems with yoke-type inerter and nonlinear dynamic absorbers based on yoke-type inerter are performed.Firstly,we present the concept of yoke-type nonlinear inerter based on the Scotch yoke mechanism and design an engineering-friendly configuration for yoke-shaped inerter.The constitutive model of the yoke-type nonlinear inerter is built based on Newton’s law and Lagrange’s equation.Subsequently,an analysis of the nonlinear inertial force characteristics of yoke-shaped inertance is conducted.A prototype yoke-type inerter is conducted and the corresponding dynamic testing is performed.The proposed constitutive model is verified through both multi-body dynamic simulations and dynamic experimental tests.Furthermore,we analyze the influence of backlash nonlinearity and qualitatively summarize the relevant influence patterns.The results of our research demonstrate that the proposed yoke-type nonlinear inerter can effectively generate apparent mass and exhibit nonlinear inertial forces as well as nonlinear negative stiffness effects.Both multi-body dynamic simulations and experimental results match well with the theoretical constitutive models,confirming the correctness of the established model.Backlash nonlinearity in the yoke-type inerter device leads to sudden changes in mechanical behavior curves.Within one cycle of harmonic motion,two sudden changes occur,with the sudden changes emerging before reaching the maximum displacement of harmonic motion.It’s worth noting that the position of these force sudden changes due to backlashes remains unaffected by variations in loading frequency for a specified loading amplitude.We recommend considering the impact of backlashes on the mechanical behavior of inerter devices during detailed performance analyses.Furthermore,the additional yoke-type inerter is proposed to improve the performance of the traditional vibration isolation system.The averaging method is employed to analytically solve the backbone curve and the dynamic response of the isolation system with yoke-type inerter under harmonic excitations.Based on the obtained analytical solutions,the dynamic characteristics and stability of the isolation system are analyzed.The vibration performances of the isolation system under both force and base displacement excitations are systematically assessed through several indices.They are dynamic response,transmissibility,effective isolation frequency bandwidth,and power flow.A comprehensive performance comparison is made among the isolation system with yoke-type inerter,the traditional isolation system,the isolation system with linear inerter,and the isolation system with nonlinear inerter using linkage mechanism.The research findings indicate that the natural frequency of the isolation system with yoke-type inerter is related to the amplitude of excitation,and decreases as the amplitude increases.When subjected to harmonic excitations,the frequency response curve of the isolation system with yoke-type inerter exhibits multiple solutions and jump phenomena at the same excitation frequency and amplitude.This indicates the need for investigation of stability issues of the system.Under both force and base displacement excitations,the addition of yoke-type inerter can effectively suppress the peak transmissibility,expanding the effective frequency bandwidth of the isolation system.Under the same nominal inertance-to-mass ratio,the isolation system with yoke-type inerter exhibits more efficient vibration isolation performance compared to the traditional isolation system,the linear inerter isolation system,and the isolation system with nonlinear inerter with linkage mechanism,offering an efficient solution for enhancing isolation system performance.Subsequently,a yoke-type inerter-based vibration absorber(YI-NLVA)is proposed to achieve high-performance vibration mitigation.The dynamic characteristics and performance of the single YI-NLVA device are analyzed.The nonlinear modes of the structure with additional YI-NLVA are solved,and the dynamic characteristics of the structure with YI-NLVA are analyzed.Under the same inertance-to-mass ratio,comparative studies on the dynamic characteristics of the structure with YI-NLVA and with linear tuned inerter damper(TID)are conducted,clarifying complex dynamic behaviors of the structure with YI-NLVA.Performance assessment using energy-based index compares the vibration mitigation performance of the structure with YI-NLVA to the structure with TID under impulsive excitations.Under harmonic excitations,the complexification-averaging method is used to analytically solve the response of the structure with additional YI-NLVA,and its vibration mitigation performance is comprehensively analyzed in comparison to the TID.The research results show that the natural frequency of the free vibration of YI-NLVA device is related to the value of the initial velocity.A higher initial velocity results in a lower natural frequency.The in-phase and out-phase vibration frequencies of the structure with additional YI-NLVA decrease as the initial input energy increases.Moreover,the configuration plane plots of the structure with YI-NLVA that are related to its nonlinear modes change from approximate linearity to significant nonlinearity as energy increases,highlighting the complexity and diversity of its dynamic characteristics and behavior.Under impulsive excitations,the structure with YI-NLVA exhibits higher energy dissipation over a broader frequency band compared to the structure with TID.Under harmonic excitations,the vibration reduction of the structure with YI-NLVA exhibits higher robustness and more efficient comprehensive performance compared to the structure with TID.Finally,case studies are conducted to assess the performance of the shipboard equipment isolation system with additional yoke-type inerter under random excitations,the base-isolated seismic isolation system with additional yoke-type inerter,and the structure with additional YI-NLVA under different levels of earthquake excitations.Under the same inertance-to-mass ratio,comparative studies are performed against relevant structural systems with linear inerter.The research results indicate that the addition of yoke-type inerter in traditional shipboard equipment isolation system effectively reduces the maximum value of the displacement response history,the maximum value of transmitted force response history,and the peak values of transmitted displacement and force functions.Moreover,when compared to the linear inerter-based equipment isolation system,the yoke-type inerter equipment isolation system exhibits superior isolation performance.Under frequent seismic events,the base-isolated system with yoke-type inerter and the structure with YI-NLVA yield almost equivalent results to those systems using linear inerters under the same inertance-to-mass ratio.However,under rare seismic events,the base-isolated system with yoke-type inerter and the structure with YI-NLVA significantly outperforms those systems using linear inerters under the same inertance-to-mass ratio.Among them,under rare earthquakes,the performance of the base-isolated system with additional yoke-type inerter is improved by an average of20%compared to the base-isolated system with additional linear inerter.For structures with vibration absorbers,the performance of the scheme with additional YI-NLVA can be improved by an average of 17%compared to the scheme with additional TID.To sum up,isolation systems with yoke-type inerters and the structure with YI-NLVA show good engineering application prospects.更多还原