Development of a graph-theory methodology for the design of vibration suppression systems

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Network-represented design possibilities of a vibration suppression system has substantially increased since the introduction of the new network element, the inerter. Classically, the most beneficial network can be determined by using one of three main approaches: structure-based, immittance-based, or evolutionary-based. The structure-based approach first proposes a network layout and then optimizes the parameter of each element according to the performance criteria. This approach is beneficial in terms of controlling the network complexity. However, this technique is limited, as there are numerous conceivable network configurations which can only be handled one layout at a time. The immittance-based approach can identify the optimal layout without restricting the network to a few specific topology arrangements. However, this method can lead to physically unrealisable networks such as: ones with an excessive number of components or ones with unfeasible component parameter values. In the evolutionary-based approach, an initial set of candidate networks is generated and iteratively updated through metaheuristics and stochastic operators. Even though this approach can automatically create a network topology that performs well, there is no assurance that the resulting network is the best possible one, nor, manufacturable considering the network complexity. A further advancement to these three traditional design techniques is a structure-immittance approach. This approach could enable the identification of the optimal vibration-absorber network with a pre-controlled complexity. In this approach, a generic network that covers all series-parallel network possibilities with a pre-determined number of element types is established; an immittance function of each network is then derived. The method sets out to control network complexities whilst achieving optimal performance measures, albeit two key constraints exist:1. The method cannot cover non-series parallel networks such as bridge networks. 2. The method is impractical to use when the number of elements being considered is large, because it couldn't be programmatically implemented.To address these two limitations, this project aims to develop a methodology based on graph theory for the design of vibration suppression systems. The novel contribution of this methodology is to allow the optimal vibration absorbers among all the possibilities with a given complexity to be identified automatically. The main objectives of this project are:To develop a methodology based on graph theory, which can provide a full set of networks for any given complexity, including series-parallel and non-series-parallel layouts. To develop a methodology which will cater to different design scenarios including multi axis systems e.g. interlinked suspensions in automotive vehicles.To physically realise the optimal network-represented properties using multi-domain components (e.g., mechanical, electrical, hydraulic and pneumatic). To establish the prototype and carry out experimental validation, so as to consolidate the proposed methodology.