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

Author:

Zhang Chengyao1,Zhao Zhiye2ORCID,Huang Haibo2ORCID,Lv Xingbing3,Lu Xi-Yun2ORCID,Yu Peng14ORCID

Affiliation:

1. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

2. Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China

3. China Nuclear Power Engineering Co., Ltd., Shenzhen, Guangdong 518172, China

4. Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

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 [Formula: see text] 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 [Formula: see text] at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical [Formula: see text] 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 [[Formula: see text], and [Formula: see text]] 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.

Funder

National Natural Science Foundation of China

China Postdoctoral Science Foundation

National Science and Technology Major Project

Shenzhen Science and Technology Innovation Commission

Publisher

AIP Publishing

Subject

Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering

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