Analytical conditions are available for the optimum design of impact absorbers for the case where the host structure is well described as rigid body. Accordingly, the analysis relies on the assumption that the impacts cause immediate dissipation in the contact region, which is modeled in terms of a known coefficient of restitution. When a flexible host structure is considered instead, the impact absorber not only dissipates energy at the time instances of impact, but it inflicts nonlinear energy scattering between structural modes. Hence, it is crucial to account for such nonlinear energy transfers yielding energy redistribution within the modal space of the structure. In the present work, we develop a design approach for reonantly-driven, flexible host structures. We demonstrate decoupling of the time scales of the impact and the resonant vibration. On the long time scale, the dynamics can be properly reduced to the fundamental harmonic of the resonant mode. A light impact absorber responds to this enforced motion, and we recover the Slow Invariant Manifold of the dynamics for the regime of two impacts per period. On the short time scale, the contact mechanics and elasto-dynamics must be finely resolved. We show that it is sufficient to run a numerical simulation of a single impact event with adequate pre-impact velocity. From this simulation, we derive a modal coefficient of restitution and the properties of the contact force pulse, needed to approximate the behavior on the long time scale. We establish that the design problem can be reduced to four dimensionless parameters and demonstrate the approach for the numerical example of a cantilevered beam with an impact absorber. We conclude that the proposed semi-analytical procedure enables deep qualitative understanding of the problem and, at the same time, yields a quantitatively accurate prediction of the optimum design.
翻译:在主机结构被明确描述为僵硬体的情况下,为最佳设计影响吸收器提供最佳分析条件;因此,分析依据的假设是,这些影响在接触区域造成立即消散,以已知的恢复系数为模型;如果考虑灵活的主机结构,其影响吸收器不仅在撞击发生时会分散能量,而且会在结构模式之间造成非线性能量散射。因此,必须说明这种非线性能源转移在结构模式空间内产生能源再分配的非线性能量转移。在目前的工作中,我们为接触区域设计一种设计方法,即以已知的恢复系数为模型;当考虑灵活的主机结构时,其影响吸收器不仅会消耗能量,而且会造成结构模式之间非线性能量散射。因此,必须说明这种非线性能源转移在结构模式内产生能源再分配。在目前的工作中,我们为重新燃起的弹性设计、灵活的主机能结构结构结构结构设计设计设计设计设计设计设计方法;我们展示这种影响的时间尺度和共振动振动的振动过程。在很长的时间尺度上,我们必须从接触力分析一个成熟的机变变的数值来,我们必须确定一个精确的数值的数值的数值的数值的数值,我们必须确定一个模拟的数值的数值变化的数值的数值的数值。