UCLA

This work begins by presenting the mathematical development of the Balakrishnan Continuum Theory (BCT) of aeroelasticity in axial flow, which was left unpublished by Professor Balakrishnan in 2015. While the mathematics and solution had been fully described, the BCT was left incomplete in the sense that it had not been implemented for engineering calculations. The methods developed as part of this dissertation for implementing the BCT are presented. To make improvements to the BCT, and to extend it, a new solution method was developed, implemented, and validated with experimental data. This method, referred to as the semi-continuum approach, combines the BCT continuum solution with a Galerkin method solution. The semi-continuum approach was applied to the fully linear problem solved by the BCT, and was consequently extended to account for nonlinear structure effects.

Experiments were performed to obtain flutter speed data, which was used to make comparisons with theoretical predictions. These comparisons demonstrate the validity of the semi-continuum approach, and the BCT that serves as its foundation. Experiments were also performed to study Limit Cycle Oscillation (LCO) in axial flow, where the dependence of the amplitude and frequencies of the oscillations on air speed was analyzed. These experiments also provide information about the shape of the structure during LCO, which was compared to the eigenfunctions produced by the semi-continuum calculations.