Tuned nonlinear spring-inerter-damper vibration absorber for beam vibration reduction based on the exact nonlinear dynamics model
Tuned nonlinear spring-inerter-damper vibration absorber for beam vibration reduction based on the exact nonlinear dynamics model
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DOI：
10.1016/j.jsv.2021.116246
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发表时间：
2021-05
影响因子：
4.7
通讯作者：
Feng Qian;L. Zuo
中科院分区：
文献类型：
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作者：
Feng Qian;L. Zuo
非线性减振器已被广泛研究用于被动振动控制、运动隔离和同步能量收集。本文研究了带有非线性弹簧-惯性阻尼器能量吸收器的简支梁的精确非线性动力学，以减少主共振振动。考虑梁的中面拉伸、结构不连续性和弹簧-惯量-阻尼器位置处的非线性边界条件，从能量法推导出系统的非线性控制方程，并使用多尺度方法直接求解。获得并研究了各种系统参数的非线性频率校正因子、频率响应函数、峰值非线性频率响应和分岔频率。研究了非线性减振器的位置、弹簧刚度、惯性质量和阻尼对梁动力学（包括固有频率、振型和非线性频率响应）的影响。非线性减振器的刚度和质量经过优化调整，以最大限度地减少梁的峰值非线性频率响应。结果表明，忽略弹簧-惯量-阻尼器位置处的非线性边界条件可能会导致非线性频率响应的严重低估。减振器的非线性刚度增强了系统非线性，但对梁的峰值非线性频率响应没有贡献。增加减振器的阻尼可以有效地减轻梁的振动。当减振器的标称频率调谐到接近梁的固有频率时，梁的振动大部分减少。
Nonlinear vibration absorbers have been extensively investigated for passive vibration control, motion isolation, and synchronous energy harvesting. This paper studies the exact nonlinear dynamics of a simply-supported beam carrying a nonlinear spring-inerter-damper energy absorber for primary resonance vibration reduction. The nonlinear governing equations of the system are derived from the energy method by considering the midplane stretching, structural discontinuity, and nonlinear boundary conditions at the spring-inerter-damper location of the beam and directly solved using the method of multiple scales. The nonlinear frequency correction factor, frequency response function, peak nonlinear frequency response, and bifurcation frequency are obtained and investigated for various system parameters. The influence of the location, spring stiffness, inertial mass, and damping of the nonlinear vibration absorber on the beam dynamics, including natural frequency, mode shape, and nonlinear frequency response, are studied. The stiffness and mass of the nonlinear vibration absorber are optimally tuned to minimize the peak nonlinear frequency response of the beam. The results show that ignoring the nonlinear boundary conditions at the spring-inerter-damper location could lead to serious underestimation of the nonlinear frequency responses. The nonlinear stiffness of the vibration absorber enhances the system nonlinearity but has no contribution to the peak nonlinear frequency response of the beam. Increasing the damping of the vibration absorber could effectively mitigate the beam vibration. When the nominal frequency of the absorber is tuned to be close to the natural frequency of the beam, the beam vibration is mostly reduced.