Dynamics and instabilities of an arbitrarily clamped elastic sheet in potential flow with application to shape-morphing airfoils

TL;DR

This paper investigates the stability and dynamics of shape-morphing elastic sheets in potential flow, focusing on interactions between segments and the effects of clamping positions, with implications for designing stable, morphing airfoils.

Contribution

It introduces a stability analysis framework for arbitrarily clamped elastic sheets in flow, revealing how segment interactions influence instability and providing design insights for shape-morphing airfoils.

Findings

Interaction between front and rear segments dominates instability.

Clamping near the leading edge increases instability.

Maximum stable speed depends on damping, fluid density, and clamp location.

Abstract

The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions, such as canceling of deflection due to aerodynamic forces and transition between two predefined cambers via continuous actuation of the airfoil. The steady results are validated by numerical calculations based on commercially available software. We then examine stability and transient dynamics by assuming small deflections and applying multiple-scale analysis to obtain a stability condition. The condition is attained via the compatibility equations of the orthogonal spatial modes of the first-order correction. The results yield the maximal stable speed as a function of elastic damping, fluid density and location of clamping. The results show that the interaction between the front and rear segments is the dominant mechanism for instability for various discrete locations of clamping. Instabilities due to interaction dynamics between the front and rear segments become more significant as the location of clamping approaches the leading edge. Several transient dynamics are presented for stable and unstable configurations, as well as instability dynamics initiated by cyclic actuation at the natural frequency of the airfoil.