A multi-scaled experimental approach for the investigation of mechanical dynamic systems

Abstract

A new scaling theory for the design of scaled experiments has appeared in the recent literature that provides rules for the combination of information from more than one scaled experiment. The new finite similitude approach introduces an infinite number of unique similitude rules that facilitate the exact transfer of information across scales. The latest adaptation of the theory additionally provides a means to assess modelling approaches to gauge their suitability under scaling. This paper introduces a new hybrid strategy with the aim to minimise the number of scaled experiments needed. This is achieved with the formation of new similitude rules that integrate scaling analysis with scaled experimentation. A consequence of the new approach is a possible reduction in the number of scales involved but at the cost of additional experiments or analysis at the remaining reduced number of scales. The concepts are developed and showcased through applications to mechanical systems formed from discrete elements of springs, lumped masses, and dampers, under the influence and action of forces, friction, and gravity. There is no limitation on the complexity of systems that can be analysed and by means of selective studies the practical value of the approach is demonstrated. A framework for scaling is established in the work with a rich set of options available to the scaled experimenter opening up new avenues of exploration unseen in the open literature.