Anisotropic scaling for thin-walled vibrating structures

• Published in: Journal of sound and vibration 2022-10, Vol.537, p.117182, Article 117182
• Main Authors: Davey, Keith, Sadeghi, Hamed, Adams, Christian, Darvizeh, Rooholamin
• Format: Article
• Language: English
• Subjects: Anisotropic scaling; Continuum mechanics; Scaling; Thin-walled structures; Vibrational analysis
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2022.117182

•Two new forms of the finite similitude scaling theory for vibration analysis.•A new high-order anisotropic space scaling approach is trialed.•The two-experiment anisotropic theory can replicate full-scale responses.•The new scaling theories can account for plate thickness change with scale.•Perfect replication for hollow sections with thickness change is shown possible.•The breaking of geometric similarity locally and globally is shown possible. 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).