Comparative analysis for optimal placement of piezoelectric actuators on smart thin plate

In contemporary smart structures, piezoelectric ceramic (PZT) actuators serve a crucial structural function. To construct a smart thin plate that integrates structural health monitoring (SHM) and active vibration control objectives, many placement methodologies were discussed. In current research, two positioning strategies of the attached PZT actuators are compared. The first strategy is a well-known controllability concept where PZT actuators' optimum positions are obtained by maximizing the eigenvalues of the controllability Grammian matrix. The second strategy employs the energy concept to strategically position PZT actuators so that the utmost amount of exerted work is accomplished by the actuators. Thus, the optimal performance of actuators to provide energy for mitigating unwanted vibrations is maintained, as is the optimal excitation required for SHM in the designated modes. Kirchoff's classical laminate plate theory (CLPT) is used to define displacements as well as the normal strains of this coupled electro-mechanical system, and then, using the Ritz solution, the modal eigenvalue problem is solved, and mode shapes are obtained. Consequently, normal strains are transformed into spatially dependent functions used to define both the virtual work and the controllability of the Grammian matrix for the PZT actuators as a function of their locations. Finally, iterative optimization based on a genetic algorithm (GA) is used to find the optimum actuator locations in the desired modes. The best location for the PZT actuator or actuators is explored for two specimen plates with different boundary conditions. The results for the two studied positioning strategies are then compared, showing the superiority of the proposed energy-based strategy. Further, a quantitative variance-based uncertainty analysis reveals a low variance of the output results for the proposed strategy.