10 July 2002 Analytic solution of a plate vibration problem controlled by piezoelectric patches
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An analytical method is given for the determination of the eigenfunctions and eigenfrequencies for two-dimensional structural vibration problems in the presence of patch sensors and patch actuators. The method is based on converting the differential equation formulation of the problem to an integral equation. The conversion is accomplished by introducing an explicit non-symmetric kernel. The kernel consists of two parts, one taking account of the stiffness and the other taking account of the control moments induced by the distributed actuators. The control moments involve piezoelectric constants and feedback voltages made up of gains times the sensor signals. Eigenfrequencies are obtained for a representative example. The results presented in the study can be used for benchmarking solutions based on numerical or approximation approaches.
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John C. Bruch, Ibrahim S. Sadek, James M. Sloss, Sarp Adali, "Analytic solution of a plate vibration problem controlled by piezoelectric patches", Proc. SPIE 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, (10 July 2002); doi: 10.1117/12.475207; https://doi.org/10.1117/12.475207

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