Passive network synthesis of restricted complexity

This dissertation is concerned with passive network synthesis in a mechanical context and applications to vehicle suspensions. This dissertation first presents a modified test for positive-realness of real-rational functions which appears only subtly different from a known condition. The test allows existing results to be derived more simply and allows more general results to be established. We then consider a realisation problem of restricted complexity where the number of dampers and inerters is restricted to one in each case, while allowing an arbitrary number of springs and no transformers (levers). The solution uses element extraction of the damper and inerter followed by the derivation of a necessary and sufficient condition for the one-element-kind (transformerless) realisation of an associated three-port network. This involves the derivation of a necessary and sufficient condition for a third-order non-negative definite matrix to be reducible to a paramount matrix using a diagonal transformation. It is shown that the relevant class of mechanical admittances can be parametrised in terms of five circuit arrangements each containing four springs. We investigate and compare the performances of the five circuit arrangements proposed when applied to suspension systems. One of the five circuits has appeared in the literature and therefore serves as the benchmark. One or more circuit arrangements appear to outperform the benchmark in terms of each individual performance measure among the three of interest and a multi-objective performance measure incorporating two of the three individual performance measures. Finally, we consider the minimum reactance synthesis of a class of biquadratic functions by reactance extraction. We show that at most four dampers are needed to synthesise the remaining resistive 3-port network when explicit conditions are met. The results are an advancement on an equivalent problem studied in the electrical network case.EThOS - Electronic Theses Online ServiceGBUnited Kingdo