A Flutter-Based Energy Harvester Device: Equations of Motion

Abstract

This paper is the first in a two-part series focused on the numerical development and integration of the equations of motion for a flutter-based energy harvesting array. The approach presented allows for modeling multiple energy harvesters arranged in spatial configurations, interacting with unsteady airflow, and coupled both aerodynamically and structurally. Each harvester in the model is characterized by six degrees of freedom, capable of experiencing significant displacements and rotations, and accommodates both rigid and elastic boundary and constraint conditions. The equations of motion are derived using a method that effectively combines Newton-Euler and Lagrangian formulations. For ease of numerical integration, these equations are represented in matrix form as a system of nonlinear, non-autonomous first-order ordinary differential equations.