有限深度介质上梁非线性能量汇减振的Winkler地基实现

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

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。

Influence of soil-structure interaction on structural dynamic characteristics is an effect with nonlinear energy sink characteristics.Here,Winkler foundation beam theory considering soil body mass was used to make finite depth elastic medium be equivalent to additional mass of a nonlinear energy sink system,and a nonlinear dynamic model of a simply supported beam system on elastic medium under harmonic excitation was established.Galerkin method and the incremental harmonic balance method were used to analyze nonlinear dynamic response of this simply supported beam on elastic medium.The correctness of the theoretical results was verified using numerical calculation method,and the effectiveness of nonlinear energy sink was analyzed.Through parametric optimization and analysis,vibration reduction effects of Winkler foundation within different parametric ranges were revealed,and optimal parametric ranges were discussed.The study results showed that within reasonable parametric ranges,elastic medium has a good suppressing effect on dynamic response of the beam supported by it,elastic medium can quickly and effectively absorb its vibration energy under resonance conditions,and have good robustness;the optimized nonlinear energy sink can reduce the beam’s resonance amplitude by over 95%,and have a wider vibration reduction frequency band;the study results reveal the vibration reduction mechanism of soil-structure interaction effect from the perspective of nonlinear energy sink to provide a theoretical basis for structural vibration suppression based on elastic foundation design.