Auto-parametric resonance presents an internal coupling means for vibration suppression, which can efficiently suppress the vibrations and decrease the amplitude spill-over peaks on both sides of the absorption band. Nevertheless, there exist problems of the single design pattern of the oscillator-pendulum structure along with broad amplitude spill-over bands. This paper puts forward a dual auto-parametric resonance-integrated absorber featuring both longitudinal-flexural and longitudinal-torsional mode coupling, unveiling a combined pattern of auto-parametric resonance for vibration absorption. Theoretical modeling and semi analytical methods are used to predict the vibration absorption performance. A longitudinal-flexural-torsional coupled dynamic model in a non-inertial frame of the system is constructed, encompassing proposing a displacement field with three generalized displacements, introducing the inextensible beam condition, deriving the constitutive relationship and attaining the governing equations via Hamiltonian variational principles. The incremental harmonic balance method (IHBM) is developed to acquire the stability boundary and amplitude-frequency bifurcation diagram of coupled dynamic systems. The results demonstrate the broadband vibration absorption performance and weakened spill-over effect under the synergy of two vibration absorption modes. It is further discovered that the mass of the absorbing beam has a substantial influence on the vibration absorption performance. The smaller the mass, the less likely it is to converge to periodic motion, yet better vibration absorption performance can be exhibited in the low frequency band.

中文翻译：

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基于双自动参数共振的宽带振动抑制，溢出效应减弱


自参共振提供了一种用于振动抑制的内部耦合手段，可以有效地抑制振动并减小吸收带两侧的振幅溢出峰值。然而，存在振荡器-摆结构的单一设计模式以及宽幅度溢出带的问题。本文提出了一种兼具纵向-弯曲和纵向-扭转模式耦合的双自参谐振集成减振器，揭示了自参谐振的减振组合模式。采用理论建模和半解析方法预测减振性能。构建了系统非惯性系中的纵-弯-扭耦合动力学模型，包括提出具有三个广义位移的位移场、引入不可延梁条件、推导本构关系并通过哈密顿变分原理得到控制方程。建立增量谐波平衡法 （IHBM） 来获取耦合动态系统的稳定性边界和幅频分岔图。结果表明，在两种减振模式的协同作用下，宽带减振性能和减弱的溢流效应减弱。进一步发现，吸收梁的质量对吸振性能有很大影响。质量越小，收敛到周期性运动的可能性就越小，但在低频段可以表现出更好的减振性能。