The scaling of nonlinear structural dynamic systems

A new scaling theory has appeared in the recent literature that has the potential to transform current approaches to scaled experimentation. The new theory introduces new similitude rules that hitherto did not exist and significantly extends the classical definition of similitude underpinned by dimensional analysis. Each new similitude rule is tied to the number of scaled experiments, and in theoretical terms there is no limit to the number of scaled experiments involved. The focus of this paper is on one and two scaled experiments applied to nonlinear structural dynamics, which is a field of study and application that gives rise to significant difficulties for scaled experimentation. The highly nonlinear behaviour common to these systems means that only very precise scaled-model designs can feasibly achieve acceptable outcomes. It is shown in the paper how the new exact similitude rules provided by the new theory deliver the precision necessary for mathematically exact replication of behaviours. It is demonstrated further how the limited scope provided by a single scaled experiment can be significantly extended by application of two properly designed scaled experiments. Through the analysis of carefully selected structural systems of one and two degrees of freedom involving nonlinear springs, dashpots and friction, the benefits of two scaled experiments are demonstrable for a range of loading conditions. Exact similitude for two scaled experiments is confirmed providing exact replication of behaviours with conformity recorded over long timescales.