Anisotropic scaling for thin-walled vibrating structures

A calculus for scaled experimentation has recently appeared in the open literature founded on the continuous (metaphysical) concept of space scaling. The new theory for isotropic scaling (termed finite similitude) is a single-parameter theory that provides similitude rules that link unlimited numbers of scaled experiments to predict the behavior of any full-scale system. A facet of the theory is that it relates scalar, vectorial and tensorial coefficients and is therefore indirectly influenced by the choice of inertial-coordinate frames characterizing the full and scaled experiments. This feature is explored in this paper to relate objects that are skewed with a particular focus on thin-walled vibrating structures, which find widespread industrial usage but also benefit from anisotropic scaling in their thickness direction. The focus here is on the recently developed first-order finite similitude theory involving two scaled-down experiments for scaled vibrational analysis. The efficacy of the proposed scaling method is examined by means of analytical and numerical simulations. Case studies involving thin-walled plates and hollow beams, subject to free and forced vibration, confirm that titanium prototypes can be represented with high accuracy (∼0% error) by scaled models of identical and different materials (viz., steel and aluminum).