Design of resonant frequencies for piezoelectric actuator with integrated components

Piezoelectric actuators are used in a wide range of electrical devices, including piezoelectric speakers, buzzers, haptics and ultrasonic transducers. For piezoelectric actuator systems used in mobile devices, the most important issue is improving the electromechanical conversion efficiency. The power consumed by the actuators must be minimized due to the small size of the batteries used. The frequency response around the mechanical resonance must be carefully designed to enable low power driving. The resonant frequencies of piezoelectric actuators that consist of integrated components, such as the metal cones in ultrasonic speakers, are determined by the energy dispersion of the total system. Therefore, factors such as the size and physical properties of each component must be designed to optimize the resonant frequencies for practical applications. The total energy of the piezoelectric system is described by Lagrange-Maxwell equations. Even though it is not easy to solve the differential equations written in a Lagrangian coordinate system by using exact calculations, useful information for designing systems can be derived from approximate calculations. In this paper, we will introduce design guidelines that can be used to optimize the resonant frequencies of piezoelectric actuators with integrated components, based on analysis using the Lagrangian coordinate system.