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F. Ziegler:
"The basis of optimal active (static and dynamic) shape- and stress-control by means of smart materials";
in: "Mechanics and Model-Based Control of Smart Materials and Structures", H. Irschik et al. (ed.); Springer Verlag, Wien, 2010, ISBN: 978-3-211-99483-2, 215 - 222.

Vibrations may shorten the lifetime of structures and machines, cause discomfort in many cases (noise radiation) and are totally unwanted in precision engineering. Reduction of the intensity level thus is of crucial importance. Application of smart materials for sensor and actuator actions is in sight. Within linear elasticity and linearized geometric relations, linear vibrations result and superposition holds good. Nonlinear optimization procedures destroy the linearity in the course of design and computational modeling. Assuming a common time function of the dynamic load, a novel approach is developed that uses the split response of the structure to the force load. Reversing the quasi-static, load-induced strain by imposing actuator eigenstrains (piezoelectric strains) not only annihilates these deformations without producing (quasi-static) stress but diminishes the dynamic part of the load deformation as well. Since it will be shown that the dynamic part of the force-produced stresses is balanced, the vibrations are fully annihilated and only the quasi-static portion of the load induced stresses remains unaffected. This optimal solution is derived within the linear theory and is thus a benchmark solution. It may serve the purpose in practical application to select properly shaped actuator patches and the control current. Even for thin-walled structures the ideal solution must be relaxed to the requirement of no additional cross-sectional resultants.