Structural analysis and control system design are combined in a unique multiobjective optimization procedure to design smart structures for the purpose of vibration suppression. This is accomplished by developing two new features for a quadrilateral finite element, and by proposing a novel method of placing the damping treatment. The first finite element feature is to embed piezoelectric material to act as sensors and/or actuators in the composite layup, and the second feature is to embed viscoelastic material in the composite layup. These three-dimensional features are implemented in such a way that they can be described with two-dimensional input. Four control algorithms are implemented: linear quadratic regulator, linear quadratic Gaussian, output feedback and proportional-derivative. The location of the damping treatment is expressed in terms of continuous design variables rather than simply checking to see whether or not an actuator is needed at a specific location. Each feature is verified to work properly. Beam and plate structures are designed for minimum mass, optimal damping ratio and minimum conglomerated modal controllability index as single objectives and in two multiobjective design environments: goal programming and fuzzy set theory. Results are found for active (piezoelectric), passive (constrained layer) and hybrid damping (active constrained layer) which indicate that the best type of damping treatment is problem dependent and all three types are worth consideration.
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