Eigenstrain Techniques for Modeling Adaptive Structures

ABSTRACT: Three-dimensional eigenstrain techniques are used in this paper to model mechanical interactions in an active structure containing small embedded sensors and actuators. Eigenstrain tech-niques are used to predict the state of the strain inside the devices (sensors and actuators) under exter-nal and internal loads. The elastic energy of the structure is written in terms of the strain inside the de-vices, and an analytical dynamic model is developed based on a generalized form of Hamilton’s variational principle. As an example, the dynamic response of an active cantilever beam containing embedded mini-devices is investigated analytically and experimentally. Specifically, active stiffness tailoring capabilities are explored. An analytical solution to the variational problem is obtained by us-ing the Raleigh-Ritz approach. A numerical example is given and the response of the active structure is verified experimentally, using a cantilever beam made of Alplex plastic as host material and piezo-electric (PZT-5H) devices as active mini-devices for sensing and actuation. The analytical results show reasonable agreement with the experimental observations