This paper mainly investigates the passive realization problems of bicubic (third-order) impedances as damper-spring-inerter networks consisting of no more than five elements. First, the special case where a bicubic impedance contains a pole or a zero on the imaginary axis or at infinity is discussed. Then, assuming that there is no pole or zero on the imaginary axis or at infinity, the realizations of bicubic impedances as five-element networks are investigated. Necessary and sufficient conditions for the realizability as five-element series-parallel networks and as five-element non-series-parallel networks are derived, respectively, where 22 series-parallel configurations and 11 non-series-parallel configurations are presented to cover the conditions. Finally, two numerical examples together with positive-real controller designs for a quarter-car suspension system are presented for illustrations. The results of this paper can contribute to the synthesis of low-complexity passive mechanical (or electrical) networks, which are motivated by the synthesis and design of inerter-based vibration control systems.

本文主要研究双三次（三阶）阻抗作为由不超过五个元素组成的阻尼器-弹簧-惯性网络的无源实现问题。首先，讨论双三次阻抗在虚轴或无穷远处包含极点或零点的特殊情况。然后，假设在虚轴或无穷远处没有极点或零点，研究双三次阻抗作为五元网络的实现。分别推导出五元串并联网络和五元非串并联网络可实现的充要条件，其中提出了22种串并联配置和11种非串并联配置，涵盖了使适应。最后，提供了两个数值示例以及用于四分之一汽车悬架系统的正实控制器设计以供说明。本文的结果有助于低复杂度被动机械（或电气）网络的合成，这是由基于惯性的振动控制系统的合成和设计驱动的。