Mathematical Aeroelasticity: A Survey

TL;DR

This survey reviews mathematical models of flow-structure interactions in aeroelasticity, analyzing conditions for flutter suppression across various regimes, boundary conditions, and modeling approaches using PDE analysis, simulations, and experiments.

Contribution

It provides a comprehensive overview of mathematical models and conditions for flutter suppression in aeroelastic systems, integrating PDE analysis, numerical, and experimental insights.

Findings

Conditions for flutter suppression identified across flow regimes.

Impact of boundary conditions on structural stability analyzed.

Role of viscous effects and modeling assumptions clarified.

Abstract

A variety of models describing the interaction between flows and oscillating structures are discussed. The main aim is to analyze conditions under which structural instability (flutter) induced by a fluid flow can be suppressed or eliminated. The analysis provided focuses on effects brought about by: (i) different plate and fluid boundary conditions, (ii) various regimes for flow velocities: subsonic, transonic, or supersonic, (iii) different modeling of the structure which may or may not account for in-plane accelerations (full von Karman system), (iv) viscous effects, (v) an assortment of models related to piston-theoretic model reductions, and (iv) considerations of axial flows (in contrast to so called normal flows). The discussion below is based on conclusions reached via a combination of rigorous PDE analysis, numerical computations, and experimental trials.