Optimal Energy Harvesting from a Membrane Attached to a Tensegrity Structure

Abstract

The feasibility of harvesting energy using polyvinylidene fluoride patches mounted on a vibrating prestressed membrane, itself attached to a tensegrity structure, was investigated. Kinematics of the tensegrity structure and the attached membrane is described and conditions for stable equilibrium for the structure are derived. Nonlinear partial differential equations describing the dynamics of the membrane attached to the tensegrity structure and under the action of a time-dependent transverse pressure are derived using the principle of virtual work. These equations are linearized and the modes of the structure are obtained using the finite element method. These modes are used as basis functions in developing a reduced-order model to obtain the response of the complete structure under the applied transverse dynamic pressure. The polyvinylidene fluoride patch on the structure is connected to an electrical load resistance. The electrical current passing through the load resistance is calculated using Gauss’s law. From this, the amount of energy available for harvesting is estimated. Next, a genetic-algorithm-based optimization is performed to find the polyvinylidene fluoride patch locations, the rest length of the tendons, and the rest dimensions of the membrane, which maximize the amount of energy that can be harvested.