Abstract
In the development of active piezoelectric/elastic structures, it was noted that a fully (symmetrically) distributed piezoelectric sensor/actuator could lead to minimum, or zero, sensing/control effects for anti-symmetrical modes of structures, especially with symmetrical boundary conditions. One method of improving the performance is to segment the symmetrically distributed sensor/actuator layers into a number of collocated sub-segments. In this chapter, mathematical models and analytical solutions of a simply supported plate with a single-piece distributed sensor/actuator and four-piece quarterly segmented sensors/actuators were derived. Modal sensitivities and modal feedback factors for the two sensor/actuator configurations are defined, and modal displacement and velocity feedbacks are formulated.
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Appendix
Appendix
Mode shapes for the first six modes, Figs. 7.17, 7.18, 7.19, 7.20, 7.21 and 7.22, of a simply supported plate. Note that there are symmetrical modes for the modes: (2,1), (3,1), (3,2), etc.
The (1,1)-th plate mode shape
The (2,1)-th plate mode shape
The (2,2)-th plate mode shape
The (3,1)-th plate mode shape
The (3,2)-th plate mode shape
The (3,3)-th plate mode shape
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Tzou, H. (2019). Distributed Control of Plates with Segmented Sensors and Actuators. In: Piezoelectric Shells. Solid Mechanics and Its Applications, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1258-1_7
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DOI: https://doi.org/10.1007/978-94-024-1258-1_7
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