Propulsive performance of oscillating plates with time-periodic flexibility

TL;DR

This study uses inviscid theory to analyze how time-periodic flexibility in oscillating plates affects swimming performance, revealing significant thrust improvements and potential instabilities.

Contribution

It introduces a theoretical framework for understanding the effects of oscillating stiffness on propulsive performance of flexible plates.

Findings

Thrust can increase by up to 35% with oscillating stiffness.

Oscillating stiffness has a lesser effect on efficiency.

Instabilities occur at high frequencies and amplitudes, possibly enhancing performance.

Abstract

We use small-amplitude inviscid theory to study the swimming performance of a flexible flapping plate with time-varying flexibility. The stiffness of the plate oscillates at twice the frequency of the kinematics in order to maintain a symmetric motion. Plates with constant and time-periodic stiffness are compared over a range of mean plate stiffness, oscillating stiffness amplitude, and oscillating stiffness phase for isolated heaving, isolated pitching, and combined leading edge kinematics. We find that there is a profound impact of oscillating stiffness on the thrust, with a lesser impact on propulsive efficiency. Thrust improvements of up to 35% relative to a constant-stiffness plate are observed. For large enough frequencies and amplitudes of the stiffness oscillation, instabilities emerge. The unstable regions may confer enhanced propulsive performance; this hypothesis must be verified via experiments or nonlinear simulations.