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On similitude law of sub-systems

Zach Liang1 and George C. Lee2

1. Department of Civil Structural and Environmental Engineering, University at Buffalo, State University of New York,
   Buffalo, New York, USA

2. Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, State University of New York,
   Buffalo, New York, USA

Abstract: Based on Buckingham's π-Theorem, dimensional analysis has achieved considerable success over the past near-century. Model testing has long been a powerful tool in both scientific studies and engineering applications. However, the prototype objects are becoming more and more complicated nowadays, and many of the prototype systems can contain several sub-systems. The conventional theories on model-prototype similarity and dimensional analysis have only limited application since the π -Theorem itself does not distinguish between the original system and subsystems. This is particularly true in the field of structural dynamics, where the structure is often modeled as a multi-degree-of-freedom system. In this paper, we attempt to show that, if a system can be decoupled into several nontrivial subsystems, then, in each subsystem, the number of π -terms will be reduced and therefore simplify the model testing. On the other hand, if a system cannot be decoupled into subsystems, then using model testing with reduced π -term analysis, both experimentally and theoretically, may introduce severe errors.

Keywords: similitude law; Buckingham's π-theorem; model testing; sub-systems