# Vibration Analysis of a Piezoelectric Ultrasonic Atomizer to Control Atomization Rate
## 1 Introduction  
Piezoelectric materials (such as lead zirconate titanate (PZT) transducers) have found broad applications in areas such as elastic vibration sensing [1], force sensing in robotics [2], ultrasonic measurements of airflow in ducts [3], and ultrasonic cleaning in energy harvesting technologies, among others. Piezoelectric materials continue to be studied to achieve better performances with lower costs and low energy requirements [4]. Important uses of piezoelectric devices include an ultrasonic atomizer for medical inhalation therapy, combustion with liquid fluids, and printed circuits, among others, where the actuator converts a liquid to atomized particles [5]. In particular, an ultrasonic atomization device is composed of a piezoelectric ceramic and a metal cover plate. It uses the piezoelectric effect and converts electrical energy into mechanical energy at a high-frequency resonance, causing the breakup of the liquid structure [6; 7; 8]. More recently, ultrasonic atomizers are being considered as replacements for pneumatic pumps for soft robotics actuation through atomization and vaporization [9]. Soft robots have recently received attention due to its flexible adaptability and the low risk of damaging the work environment and the objects they handle. Many soft robots require small external compressors or pumps for driving the actuator. Actuator miniaturization could be achieved with the use of an ultrasonic atomizer. For example, [PERSON] and [PERSON] [10] proposed a soft inflatable one-DOF (degree of freedom) robot. It has a soft bellows structure that includes a lower chamber with an embedded ultrasonic atomizer of only 15 mm in diameter and a heater to evaporate the atomized liquid and to control the vertical displacement of the soft robot. In this system, the modes of vibration and resonance frequencieshave a direct effect on the displacement and actuation speed. Thus, there is a need to develop a more comprehensive vibration analysis and mesh properties to have an optimum control of the soft robot compliance control. Tuning of the frequency and vibration parameters is a main objective in the design and optimization of an ultrasonic transducer. There are conventional methods to calculate the modes in the free vibration of a plate, but they are limited to plates that have a continuous homogenous structure without changes in the cross-section. Additionally, there are methods to numerically approximate the modes of a vibration, for example, using the plane wave expansion method [11]; however, it can be computationally complex for inhomogeneous models. In addition, the coupling effect of piezoelectric energy with mechanical energy needs to be considered, making the theoretical analysis and its general solution difficult to obtain. With the increase in the computational capacity, numerical approximations of the piezoelectric phenomena can be studied using finite element (FE) methods. A typical structure of an ultrasonic atomizer is described in Figure 1. A main component of the system is the mesh (i.e., light gray section), which is formed by a thin plate with a thickness of 50 \(\upmu\)m and micro-perforations. The holes are distributed within a circular area with a diameter \(D_{a}\). The ring is the piezoelectric actuator (e.g., PZT) with a thickness of about 0.6 mm. A potential difference (voltage) is applied to the piezoelectric ring across the thickness using a signal generator. \(D_{in}\) and \(D_{out}\) are the inner and outer diameters of the piezoelectric ring, respectively, and \(D_{a}\) is the diameter of the disperser or mesh. The objectives of this work are to first characterize the dynamic behavior of the complete piezoelectric ring and meshed thin plate using FE modeling. Second, the effect of the shape of the micro-apertures on the resonant frequency spectra of the vibrating thin plate is investigated. Last, the numerical simulation results of the atomization rate as a function of the frequency response and voltage are verified using experimental tests.