On the assumptions and decisions required for reduced order modelling of engineering dynamical systems
This paper considers the principal assumptions and decisions that have to be made when developing reduced order models of problems in engineering dynamics. The work has been motivated by a perception that information loss can be considerable when applying approximate analytical solution methods, despite good solutions per se being obtainable with appropriate application. The lost information relates to the evolution of solutions and the consequential inheritance issues. Simplifications, which are normally routinely made during approximate analytical solution, irrespective of the method used, can remove an additional layer of information from the solution. This information is apparently redundant when structural simplification is the principal objective, but if it is retained it can show how the solution has come together, all the principal influences that are acting, and how they interact with each other. This paper takes 10 sample problems in engineering dynamics and highlights the many common and different modelling assumptions that are needed to generate viable and realistic equations of motion, from which inheritance based approximate analytical solutions can be generated, and ultimately visualised.