Modeling and Optimization of Passively Damped Adaptive Composite Structures

A smart structural model is used to optimally determine both the placement of piezoelectric actuators and parameters describing associated electrical components in a passively damped structure. The technique utilizes a recently developed coupled piezoelectric-mechanical theory to analytically determine the response of arbitrary structures with piezoelectric materials and attached electrical circuitry. The theory simultaneously models both the structural and the electrical components, and the complex state of strain that may exist in the piezoelectric patches, thereby providing accurate mechanical and electrical response. A robust multiobjective optimization procedure is developed to design the passive system for simultaneous damping of several critical modes of interest. The influence of stacking sequence in augmenting passive damping can also be examined by including ply orientations as design variables. Since the optimization problem now involves both continuous and discrete design variables, a hybrid optimization technique is used that allows the inclusion of both types of design variables. Also, since multiple design objectives are introduced, the Kreisselmeier-Steinhauser function approach is used allowing the multiple and conflicting design objectives and constraints to be combined into a single unconstrained function. Results demonstrate the ability of this technique to determine the optimal tuning parameters for damping of multiple modes of vibration using a limited number of piezoelectric actuators.