Similitude theory allows engineers, through a set of tools known as similitude methods, to establish the necessary conditions to design a scaled (up or down) model of a full-scale prototype structure. In recent years, to overcome the obstacles associated with full-scale testing, such as cost and setup, research on similitude methods has grown and their application has expanded into many branches of engineering. The aim of this paper is to provide as comprehensive a review as possible about similitude methods applied to structural engineering and their limitations due to size effects, rate sensitivity phenomena, etc. After a brief historical introduction and a more in-depth analysis of the main methods, the paper focuses on similitude applications classified, first, by test article, then by engineering fields.

The scope of this work is to consolidate research dealing with the vibroacoustics of periodic media. This investigation aims at developing and validating tools for the design and characterization of global vibroacoustic treatments based on foam cores with embedded periodic patterns, which allow passive control of acoustic paths in layered concepts. Firstly, a numerical test campaign is carried out by considering some perfectly rigid inclusions in a 3D-modeled porous structure; this causes the excitation of additional acoustic modes due to the periodic nature of the meta-core itself. Then, through the use of the Delany–Bazley–Miki equivalent fluid model, some design guidelines are provided in order to predict several possible sets of characteristic parameters (that is unit cell dimension and foam airflow resistivity) that, constrained by the imposition of the total thickness of the acoustic package, may satisfy the target functions (namely, the frequency at which the first Transmission Loss (TL) peak appears, together with its amplitude). Furthermore, when the Johnson–Champoux–Allard model is considered, a characterization task is performed, since the meta-material description is used in order to determine its response in terms of resonance frequency and the TL increase at such a frequency. Results are obtained through the implementation of machine learning algorithms, which may constitute a good basis in order to perform preliminary design considerations that could be interesting for further generalizations.

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Up to now, similitude methods have been used in order to overcome the typical drawbacks of experimental testing and numerical simulations by reconstructing the full-scale model behavior from that of the scaled model. The novelty of this work is the application of similitude theory not as a tool for predicting the prototype dynamic response, but for supporting, and eventually validating, experimental measurements polluted by noise. Two Aluminium Foam Sandwich (AFS) plates are analyzed with Digital Image Correlation (DIC) cameras. First, an algorithm for blind source separation problems is used to extract information about the excitation; then, SAMSARA (Similitude and Asymptotic Models for Structural-Acoustic Research Applications) similitude method is applied to both the force spectra and velocity responses of prototype and model. The reconstruction of force and velocity curves demonstrates that the similitude results are coherent with the quality of the experimental measurements: when the spatial pattern in resonance is recognizable, then the curves overlap. Instead, when the displacement field of just one model is not well identified, the reconstruction exhibits discrepancies. Therefore, similitude methods reveal to be an interesting tool for understanding if a set of measurements is reliable or not and their application should not be underestimated, especially in the light of the expanding range of approaches which can extract important information from noisy observations.