Measuring the flexibility matrix of an eagle’s flight feather and a method to estimate the stiffness distribution*

Abstract

Flight feathers stand out with extraordinary mechanical properties for flight because they are lightweight but stiff enough. Their elasticity has great effects on the aerodynamics, resulting in aeroelasticity. Our primary task is to figure out the stiffness distribution of the feather to study the aeroelastic effects. The feather shaft is simplified as a beam, and the flexibility matrix of an eagle flight feather is tested. A numerical method is proposed to estimate the stiffness distributions along the shaft length based on an optimal Broyden–Fletcher–Goldfarb–Shanno (BFGS) method with global convergence. An analysis of the compressive behavior of the shaft based on the beam model shows a good fit with experimental results. The stiffness distribution of the shaft is finally presented using a 5th order polynomial.