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Eigenstrain Techniques for Modeling Adaptive Structures: II. Active Damping

This is the second paper, in a two-part series, that demonstrates the utility of Eshelby’s eigenstrain techniques for modeling adaptive structures. The first paper addressed adaptive stiffening (Alghamdi and Dasgupta, 2000). The objective of this second paper is to model adaptive damping. Distributions of small active piezoceramic 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 the converse piezoelectric effect. The coupled electromechanical boundary value problem is solved using a generalized form of Hamilton’s principle where the energy functional is evaluated using the eigenstrain method. System dynamic equations are developed for active damping and a numerical solution to the variational problem is obtained by using the Raleigh-Ritz approach. Numerical results are verified experimentally using a cantilever beam with distributions of embedded piezoelectric (PZT-5H) mini-devices. A significant amount of damping is achieved for low volume fraction of devices and good agreement is obtained between numerical and experimental results. The eigenstrain technique is demonstrated to be a capable three-dimensional tool for modeling adaptive structures with embedded distributions of mini-devices.