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Eigenstrain Techniques for Modeling Adaptive Structures. I: Active Stiffness Tailoring

Three-dimensional eigenstrain techniques are used in this paper to model mechanical interactions in an active structure containing small embedded sensors and actuators. Eigenstrain techniques are used to predict the state of the strain inside the devices (sensors and actuators) under external and internal loads. The elastic energy of the structure is written in terms of the strain inside the devices, 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 using 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 piezoelectric (PZT-5H) devices as active mini-devices for sensing and actuation. The analytical results show reasonable agreement with the experimental observations.