For a nonlinear beam under broadband excitations, the multimodal nonlinear resonance phenomena will be induced. To suppress the multimodal nonlinear resonances, the multiple time-delayed vibration absorbers (TDVAs) are introduced. The optimal time-delayed parameters of the TDVAs are determined by the proposed multimodal equal-peak principle consisting of three design criteria. In the proposed three criteria, the stability criterion ensures the stability of the equilibrium state for the system; the extremes equal criterion figures out the time-delayed parameters to realize the equal resonance peaks around each concerned mode; the minimum peak criterion can obtain the optimal time-delayed parameters for the minimum resonance peaks. The results show that the TDVAs designed by the proposed multimodal equal-peak principle consisting of three criteria could simultaneously suppress the resonance peaks of the beam around multiple modes to the equal and minimum values. Besides, the equal resonance peaks are much lower than the absorbers without time-delayed feedback under the same mass constraint. The proposed TDVAs and the multimodal equal-peak principle have wide application prospects in suppressing the multimodal vibrations for nonlinear continuous systems with broad frequency band and large amplitudes excitation in the fields of civil engineering and aerospace.

对于宽带激励下的非线性梁，会引起多模态非线性共振现象。为了抑制多模态非线性共振，引入了多个延时减振器 (TDVA)。TDVA 的最佳延时参数由提议的多峰等峰原理决定，该原理由三个设计标准组成。在提出的三个准则中，稳定性准则保证了系统平衡状态的稳定性；极端相等判据计算出时滞参数，以实现每个相关模式周围的相等共振峰；最小峰值判据可以得到最小共振峰的最佳时延参数。结果表明，由提出的由三个标准组成的多模态等峰原理设计的 TDVA 可以同时将多模态周围梁的共振峰抑制到相等和最小值。此外，在相同质量约束下，等共振峰远低于没有时滞反馈的吸收器。所提出的TDVAs和多峰等峰原理在土木工程和航空航天领域的宽频带和大振幅激励非线性连续系统的多峰振动抑制方面具有广泛的应用前景。在相同质量约束下，相等的共振峰远低于没有延时反馈的吸收器。所提出的TDVAs和多峰等峰原理在土木工程和航空航天领域的宽频带和大振幅激励非线性连续系统的多峰振动抑制方面具有广泛的应用前景。在相同质量约束下，相等的共振峰远低于没有延时反馈的吸收器。所提出的TDVAs和多峰等峰原理在土木工程和航空航天领域的宽频带和大振幅激励非线性连续系统的多峰振动抑制方面具有广泛的应用前景。