In this study, a generalized equal-peak principle is established to suppress the multimodal vibration of a multiple-degree-of-freedom (M-DOF) nonlinear system. Based on the proposed generalized principle, the design procedure of the multiple time-delayed vibration absorbers (TDVAs) is carried out. By four conditions in the proposed generalized principle, the objective of suppressing all the resonance peaks around multiple modes to the equal minimum values is realized. For the existence of nonlinearity, the necessary and sufficient conditions in the design procedure can guarantee that the two resonance peaks around each mode are simultaneously equal. Moreover, the two equal resonance peaks are suppressed to minimum values with the minimum peak condition. Two case studies verify the efficiency of the TDVAs designed by the generalized equal-peak principle for multimodal vibration suppression. Due to the multimodal vibration suppression capacity of the proposed TDVAs designed by the generalized equal-peak principle, significant broad frequency band vibration suppression effects are achieved. Thus, TDVAs and the proposed equal-peak principle have potential applications in the fields of high-DOF vibration systems, such as civil engineering, precision machining and aerospace.

在这项研究中，建立了广义等峰原理来抑制多自由度（M-DOF）非线性系统的多模态振动。基于提出的广义原理，进行了多个时滞减振器（TDVA）的设计程序。通过提出的广义原理中的四个条件，实现了将多个模式周围的所有共振峰抑制到相等的最小值的目的。对于非线性的存在，设计过程中的充要条件可以保证每个模式周围的两个共振峰同时相等。而且，两个相等的共振峰在最小峰条件下被抑制到最小值。两个案例研究验证了通过广义等峰原理设计的TDVA的多模态振动抑制效果。由于采用广义等峰原理设计的TDVA具有多模态的抑振能力，因此可实现明显的宽带抑振效果。因此，TDVA和提出的等峰原理在高自由度振动系统领域中具有潜在的应用，例如土木工程，精密加工和航空航天。