A Graph-Based Methodology for Optimal Design of Inerter-Based Passive Vibration Absorbers With Minimum Complexity

Passive vibration absorbers (PVAs) play a crucial role in mitigating excessive vibrations in engineering structures. Traditional PVA design typically begins with proposing a beneficial topological layout, incorporating stiffness, damping, and inertance elements, followed by optimal sizing of each element to minimise specific response of dynamically excited structures. An alternative approach involves first designing the impedance function of a PVA and then identifying a passive mechanical layout that replicates this impedance using network synthesis techniques. However, both methods struggle to identify the most efficient PVA layout using the minimum number of elements (referred to as “complexity”) for a given vibration suppression problem. To this end, this study introduces a graph-based methodology for designing optimal configurations (i.e., layout + sizing) of two-terminal spring-damper-inerter PVAs that achieve specified performance goals with minimum complexity. In this approach, a PVA is represented as a weighted coloured multigraph, enabling the application of a novel graph-based enumeration technique to generate the full set of potential layouts from any given number of mechanical elements. This enumeration is followed by a performance assessment of all layouts to pinpoint the optimal absorber configuration for the given problem. The methodology’s automation capability and versatility make it suitable for various civil and mechanical engineering applications. The effectiveness of the proposed methodology is demonstrated through two case studies: a vibration absorber design for a wind-excited tall building and a suspension design for a road vehicle. In both cases, the proposed methodology successfully identifies innovative PVA layouts that surpass traditional designs with minimum additional elements.