Wave-like modelling of cascaded, lumped, flexible systems with an arbitrarily moving boundary

This paper considers cascaded, lumped, flexible systems, which may be short and non-uniform, which are driven by an arbitrarily moving boundary. Such systems exhibit vaguely wave-like behaviour yet defy classical wave analysis. The paper proposes novel ways to analyse and model such systems in terms of waves. It presents two new wave models for non-uniform systems, one series and one shunt, defining their component wave transfer functions, and thereby providing a way to define, identify and measure component waves. Features of the models are compared. The series and shunt configurations are mutually consistent and can be combined into a single composite wave model. The models are exact, but elements within them remain arbitrary to some degree, implying slight differences in the wave decomposition of the system. Some good model choices are proposed and explored. Wave speed and wave impedance are briefly considered, as are ways to measure component waves. Implications are discussed.