有限深度介质上梁非线性能量汇减振的Winkler地基实现

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (1) : 237-245.

论文

刘宗通1，马建军1,2，郭颖1

作者信息 +

Nonlinear energy sink for vibration reduction of a beam on finite depth medium based on Winkler foundation

LIU Zongtong1, MA Jianjun1,2, GUO Ying1

Author information +

文章历史 +

摘要

土-结构相互作用对结构动力学特性的影响是一种具有非线性能量汇特征的效应。利用考虑土体质量的Winkler地基梁理论，将有限深度弹性介质等效为非线性能量汇系统的附加质量，建立简谐激励下弹性介质上简支梁系统的非线性动力学模型。采用Galerkin方法和增量谐波平衡法分析了弹性介质上简支梁的非线性动力响应。利用数值计算方法验证了理论结果的正确性，并分析了非线性能量汇的有效性。通过参数优化和分析，揭示了不同参数范围内Winkler地基的减振效果，讨论了其最佳参数范围。研究结果表明：在合理的参数范围内，弹性介质对其支承梁的动力响应有良好的抑制作用，能够快速有效地吸收共振条件下的振动能量，并具有良好的鲁棒性。优化后的非线性能量汇可使梁的共振幅值降低超95%，且具有较宽的减振频带。研究成果从非线性能量汇的角度展现了土-结构相互作用效应的减振机理，为基于弹性地基设计的结构振动抑制提供了理论依据。

Abstract

The effect of soil-structure interaction on structural dynamics is a nonlinear energy sink. Using Winkler foundation beam theory considering soil mass, the limited depth elastic medium is equivalent to the additional mass of the nonlinear energy sink system. The nonlinear dynamic model of the supported beam system on the elastic medium under harmonic excitation is established. The Galerkin and incremental harmonic balance method analyze the nonlinear dynamic response of a supported beam on the elastic medium. The correctness of the theoretical results is verified by numerical calculation, and the effectiveness of the nonlinear energy sink is analyzed. The vibration reduction effect of the elastic medium in different parameter ranges is revealed through parameter optimization and analysis, and the optimal parameter range is discussed. The results show that the elastic medium has an excellent inhibitory effect on the dynamic response of the supporting beam within a reasonable parameter range. It can quickly and effectively absorb the vibration energy under resonance conditions and has good robustness. The optimized nonlinear energy sink can reduce the resonance amplitude of the beam by more than 95% and has a wide vibration reduction frequency band. The research results show the vibration reduction mechanism of soil-structure interaction from a nonlinear energy sink perspective and provide a theoretical basis for structural vibration suppression based on the elastic foundation design.

导出引用

刘宗通1，马建军1,2，郭颖1. 有限深度介质上梁非线性能量汇减振的Winkler地基实现[J]. 振动与冲击, 2024, 43(1): 237-245

LIU Zongtong1, MA Jianjun1,2, GUO Ying1. Nonlinear energy sink for vibration reduction of a beam on finite depth medium based on Winkler foundation[J]. Journal of Vibration and Shock, 2024, 43(1): 237-245

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