A Unified Dynamic Similitude of Solid Continuum and its Application in Aeroelastic Structures

Abstract

Copyright © 2022 The Authors. The use of dynamic similitude has been widely proven in fluid mechanics. With the drive for efficient aircraft wing through high aspect ratio wings comes the growing need for much more accurate aeroelastic analyses of aircraft wings and more accurate scaled experimental tests. Even with this need for dynamic similitude in solid mechanics, there is still no unified exact scaling law applicable to any given solid structure or system. Here we present a recently proposed unified similitude model for solid mechanics using the momentum and the energy conservation. The model allows for the use of different materials in both elastic and plastic regimes. Never reported dimensionless numbers are derived for the first time in this article, and this set of numbers is sufficient for strictly accurate dynamic similitude of any solid structure. The application of the unified model is demonstrated for the first time in an aeroelastic structure and in aerospace structures through case studies. The very good agreement seen in compared results confirms the accuracy of the developed scaling model and the exactness of the dimensionless numbers.