Effect of non-uniform stiffness distribution on the dynamics of inverted plates in a uniform flow

Abstract

The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading edge's bending stiffness K∗ and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of K∗ at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical K∗ derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plates and non-uniform plates. Moreover, three orders of mass ratio [O(10−2), O(10−1), and O(1)] are investigated, and the underlying mechanism for large amplitude flapping is clarified for the inverted plate with different mass ratios. An appropriate bending stiffness distribution can greatly improve the deformation of the plate. The findings shed some light on the energy harvesting of the inverted plate.