Active Vibration Control Using Optimized Piezoelectric Topologies

This work investigates the optimal topology of an actively controlled piezoelectric actuator bonded to an elastic cantilever beam under steady-state harmonic loading near the first natural frequency of the beam. The actuator is discretized using finite elements, and control is applied to the actuator based on the sensor’s degrees of freedom using proportional control. This study investigates the optimal distribution of actuator material for one and five layers of finite elements. The optimized actuator topology shows substantial improvement over initial piezoelectric topologies and over traditional actuator placement. This study has two main topics, material homogenization and topology optimization. The piezoelectric actuator is homogenized to determines it’s relation to volume fraction of material. This continuous relationship to volume fraction is a more “realistic” material variation compared with the typical artificial material model used in topology optimization. The actuator topology of the actuator is optimized to minimize the vibration amplitude. To the author’s knowledge, little work has focused on the optimal topologies of a piezoelectric actuator to minimize the amplitude displacement at the first mode of a cantilever beam.