PERFORMANCE ANALYSIS AND STABILITY STUDY OF DIFFERENT TYPES OF NONLINEAR VIBRATION ABSORBERS WITH COMBINED STIFFNESS OF HORIZONTAL SPRINGS
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摘要: 动力吸振器作为一种振动控制单元被广泛运用于各种工程场合, 但传统的线性吸振器只能实现窄带振动控制. 文章在线性吸振器的基础上引入对称水平弹簧构建线性刚度与非线性刚度相结合的组合刚度非线性吸振器, 以提升吸振器的吸振性能. 考虑实际工程中可能的安装方式, 分别建立水平弹簧接地安装和不接地安装的组合刚度非线性吸振器模型, 利用谐波平衡法结合弧长延拓法解析求解动力学响应, 并与数值结果相互验证, 证明了求解结果的准确性. 随后分析比较两种组合刚度非线性吸振器与线性吸振器以及非线性能量阱之间的吸振性能, 发现水平弹簧接地安装类型的组合刚度非线性吸振器在保留线性吸振器优势的同时又改善其吸振频带窄的缺点, 且与非线性能量阱相比在主共振频率附近的较宽频内吸振性能更优. 在此基础上, 讨论了水平弹簧参数以及吸振器阻尼对主结构振动幅频响应和稳定性的影响, 最后观察分析主结构幅频响应曲线不稳定区内的复杂动力学行为. 研究结果表明合适的设计参数能够使得主结构振动峰值较低的同时, 频响曲线不稳定运动区域的范围也较小.Abstract: As a kind of vibration control unit, dynamic vibration absorber is widely used in various engineering situations, but the traditional linear vibration absorber can only achieve narrow band vibration control. On the basis of the linear vibration absorber, this paper introduces symmetrical horizontal springs to build a combined stiffness nonlinear vibration absorber with linear stiffness and nonlinear stiffness to improve the vibration absorption performance of the absorber. Considering the possible installation modes in actual projects, the combined stiffness nonlinear vibration absorber models of horizontal spring with grounding and without grounding are established respectively. The dynamic response is solved analytically by the harmonic balance method combined with the arc length continuation method, and the results are mutually verified with the numerical results, which proves the accuracy of the solution results. Then, the vibration absorption performance between two kinds of combined stiffness nonlinear vibration absorbers, the linear vibration absorber, and the nonlinear energy sink is analyzed and compared. It is found that the combined stiffness nonlinear vibration absorbers with horizontal spring grounding installation type not only retain the advantages of the linear vibration absorber, but also improve the shortcomings of its narrow vibration absorption frequency band. In addition, the combined stiffness nonlinear vibration absorber of horizontal springs grounding installation type has better vibration absorption performance in a wider frequency band near the main resonance frequency than the nonlinear energy sink. On this basis, the effects of horizontal spring parameters and absorber damping on the amplitude-frequency response and stability of the main structure are discussed. Finally, the complex dynamic behavior in the unstable region of the amplitude-frequency response curve of the main structure is observed and analyzed. The research results show that the appropriate design parameters can make the vibration peak value of the main structure low, and the unstable movement area of the frequency response curve is also small.
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Key words:
- combined stiffness /
- nonlinear vibration absorber /
- horizontal spring /
- installation form /
- stability
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图 1 线性吸振器两端安装水平弹簧
Figure 1. Horizontal springs are installed at both ends of the linear vibration absorber
图 2 非线性恢复力与刚度特性: (a)非线性恢复力曲线和(b)非线性刚度特性曲线
Figure 2. Nonlinear restoring force and stiffness characteristics. (a) Nonlinear restoring force curve and (b) nonlinear stiffness characteristic curve
图 5 两种安装形式的幅频特性曲线比较
Figure 5. Comparison of amplitude-frequency characteristic curves of two installation forms
图 9 水平弹簧预压缩长度变化的影响
Figure 9. Influence of horizontal spring pre-compression length change
图 12 不同观测点下的时域图、相轨迹和庞加莱点
Figure 12. Time domain diagram, phase trajectory and Poincare point under different observation points
表 1 系统模型参数表
Table 1. Table of model system parameters
Parameter Variable Value main mass m1/ kg 100 main structure stiffness k1/(N·m−1) 4 × 105 main structure damping c1/(N·s·m−1) 253 mass of vibration absorber m2/ kg 10 vertical spring stiffness k2/(N·m−1) 1.47 × 105 vibration absorber damping c2/(N·s·m−1) 50 horizontal spring stiffness k3/(N·m−1) 4.8 × 105 original length l0/m 0.04 precompression length l/m 0.036 external excitation amplitude F0/N 140 
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