Response of adaptive structures with multiple embedded devices using eigenstrain techniques

The main objective of this dissertation is to model the mechanical interactions in adaptive structures using eigenstrain techniques. The devices embedded in the adaptive structure are treated as elastic heterogeneous inclusions. Sensors are treated as elastic heterogeneities subjected to external loads, whereas actuators are modeled as elastic heterogeneities subjected to both external loads and internal induced strains caused by peizoelectricity effect. The mathematical modeling is performed for uniform and nonuniform (linear) distributions of external applied loads. The coupled electromechanical boundary value problem is solved using a generalized version of Hamilton's principle where the energy functionals are evaluated using the eigenstrain method. System dynamic equations are developed for adaptive stiffening and adaptive damping, and the Rayleigh-Ritz technique is used to approximate the behavior of the structure.; Results obtained for an adaptive beam are verified experimentally using a simple cantilever beam made of Alplex plastic material with embedded piezoelectric (PZT-5H) sensors and actuators. Experimental results show the same trend as the model predictions. These results illustrate the power of eigenstrain technique to model adaptive structures with embedded micro-devices. Modeling the far-field (mechanical) loading as uniform inside micro-devices is found to be adequate, as the contribution of linear term is minimal for dilute distribution of devices. Adaptive stiffening is found to increase the effective stiffness of the beam by a low amount, while adaptive damping significantly increases the effective damping of the beam, for the low volume fraction of devices considered in the study.