This study is concerned with the problem of analysis and optimization of inerter-based systems. A main inerter system is generally composed of an inerter, a spring, and viscous damper. Series–parallel inerter systems and series inerter systems are two commonly used configurations of inerter-based systems. First, in this study, the H_∞ optimum parameters of inerter-based isolators are derived to minimize the compliance and mobility transfer function of a single-degree-of-freedom system under a harmonic ground acceleration excitation. Under the optimum tuning condition, it is shown that the proposed inerter-based isolators when compared with the traditional dynamic vibration absorber provide larger suppression of the peak value of the magnitude of compliance and mobility transfer functions of the primary system. For the studied cases, more than 40% and 45% improvement can be attained in terms of minimizing the compliance and mobility transfer functions, respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 15% and 11% improvement can be attained respectively, for the series inerter system. Finally, further comparison between the inerter-based isolators and traditional dynamic vibration absorber under white noise excitation also shows that the series–parallel inerter system and series inerter systems are superior to the traditional dynamic vibration absorber. The results of the studied systems show that more than 23% and 16% improvement are attained in terms of minimizing the compliance and mobility transfer functions respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 26% and 13% improvement can be attained respectively, for the series inerter system. The optimal parameters for different cases are obtained. It is shown that the optimal parameters obtained using the minimized mobility transfer function are smaller than those using the compliance transfer function at all mass ratios or inertance-to-mass ratio. The results of this study can provide theoretical basis for design of the optimal inerter-based isolators in engineering practice.

这个 研究 与基于惯性系统的分析和优化有关。主惰道系统通常由惰道，弹簧和粘性阻尼器组成。 系列–平行惰性系统s 串联惯性系统s 通常是两个 用过的 基于惯性系统的配置s。第一， 在这 研究， ^ h _∞ 推导了基于惯性的隔离器的最佳参数，以最大程度地降低柔性和迁移率传递函数 单学位谐波地面加速度激励下的自由系统。下 的 最佳调谐条件，表明与传统的动态吸振器相比，拟议中的基于惯性的隔离器可以更大程度地抑制柔度和迁移率传递函数的峰值s 主系统。对于所研究的案例，就最小化顺应性和迁移率传递功能而言，可以实现40％和45％以上的改进s与传统的相比 动态吸振器 为了 系列–平行惰性系统 分别可以提高15％和11％， 为了 串联惰性系统。最后，基于惯性的隔离器与传统隔离器之间的进一步比较 动态吸振器 在白噪声激发下也表明 系列–平行惰性系统 和 串联惰性系统s 优于传统 动态吸振器。研究系统的结果表明 米在使法规遵从性和流动性转移功能最小化方面，矿石分别提高了23％和16％s 分别， 与 的 传统的 动态吸振器 对于 的 系列–平行惰性系统 分别可以提高26％和13％， 为了 串联惰性系统。获得了针对不同情况的最佳参数。结果表明，在所有质量比或惯性质量比下，使用最小迁移率传递函数获得的最优参数均小于使用顺应性传递函数获得的最优参数。研究结果可为工程实践中最佳基于惯性的隔离器设计提供理论依据。