The analysis of scaled mechanical dynamic systems

A new approach to scaled experimentation has appeared in the open literature bringing into existence a countably infinite number of similitude rules connecting multiple scaled experiments. The simplest rule (the zeroth-order rule) captures all what is possible with dimensional analysis but higher-order rules appear to necessitate investigations at multiple scales. The scaling theory finite similitude can however, be repurposed for the analysis of scaled models making it possible to relate models of two different sizes whilst automatically accounting for all scale effects present. The new approach to scaling analysis gives rise to additional systems of equations that are required to be solved and it is this aspect that is the main focus of this paper. It is shown through application of the new scaling-analysis approach to mechanical systems built from discrete elements (e.g., springs, lumped masses, dampers) how scale effects are directly represented. Scaling analysis under the finite-similitude framework is shown to be effective for connecting up scaled models but additionally dovetails with experimental approaches involving scaled experiments. Through application to mechanical systems the new formulation is shown to have practical value but also reveals how system-level scale effects can be handled efficiently. The approach provides a framework for the design and analysis of mechanical components that are required to operate over a range of sizes.