Energy-Based Optimal Placement of Piezoelectric Actuator on Smart Thin Plate

Abstract

Purpose To establish a smart thin plate in which structural health monitoring (SHM) and active vibration control purposes are integrated, the locations of attached piezoelectric ceramic (PZT) actuators as well as their applied normalized voltage are investigated. Method Normal strains of such coupled electro-mechanical systems are defined using Kirchoff's classical laminate plate theory (CLPT), and then, by Ritz solution, these normal strains are converted to spatially dependent functions that are employed to define virtual work for the actuators as a function of location and applied voltage. Finally, genetic algorithm (GA)-based iterative optimization is carried out to locate the actuators as well as determine the normalized applied voltage for each of them in the desired modes. Results Three plates with different boundary conditions are studied for optimal placement of PZT actuator/s . The PZT actuator/s are optimally placed where the maximum amount of exerted virtual work is reached to fulfil the perfect excitation needed by SHM and provide the highest damping energy for undesired vibration at designated modes. The results show that the optimum location of PZT actuator/s lies where the maximum sum of normal strains is. Conclusion The proposed process is valid for any mixed boundary conditions on a thin plate with any number of square actuators with a minimum computational effort, where both location of the actuator/s and applied voltage can be manipulated via GA to achieve the maximum exerted work done by PZT actuator/s at each desired natural mode.