## 1 Introduction  
Microporous piezoelectric ultrasonic atomization is a new type of ultrasonic atomization method, which is the process of using the high-frequency vibration of piezoelectric ceramics to force the continuous fluid to disperse into two-phase flow and further disperse into droplets through micropores. Microporous piezoelectric ultrasonic atomizers can be divided into static and dynamic mesh atomizers according to whether the microporous plate vibrates [1, 2]. These types of atomizers have their own advantages and disadvantages, but compared with static mesh atomizers, dynamic mesh atomizers do not need a liquid cavity with variable volume, greatly simplifying the structure and effectively solving the problems of the low energy utilization rate and large droplet size. In addition, given its advantages, such as low cost, low energy consumption, and uniform atomizing particle size, dynamic mesh atomizers have been widely used in air humidification, spray cooling, biomedicine, aromatherapy, atomizing inhalation therapy, and other fields [3; 4; 5; 6; 7; 8; 9; 10]. In recent years, in order to explore the factors affecting the atomization effect of dynamic mesh atomizers, researchers in different application fields have adopted theoretical analysis, simulation, experimental research, and other methods. [PERSON] et al. proposed a dynamic mesh atomizer and found through experiments that the atomization quantity of the atomizer is proportional to the number of pinholes, and the atomization quantity at the second-order resonant frequency is larger than that at the first-order frequency [11]. Microtapered apertures were first used instead of pinholes by [PERSON] et al., and the water supply structure of the atomizer was also eliminated to reduce the volume of the device [12; 13]. [PERSON] et al. used the finite element method to optimize the design of atomizing sheet and thus developed the technology of using the atomizer to deposit ink, organic polymers, and solid particles [14; 15; 16; 17; 18]. [PERSON] et al. studied an atomizing device with a symbol-type high power driver to realize the atomization of lavernder oil, proving that the atomizer can realize the atomization of high viscosity liquid (cP \(>\) 3.5) [19]. [PERSON] et al. found through experiments on the influence of the change in the cone angle in the vibration of the atomizing sheet on the atomization performance and thus proposed the theory of the dynamic cone angle for the first time [20]. Later, [PERSON] et al. studied the influence of the vibration characteristics of the atomizing sheet on the atomization performance at different resonant frequencies through simulation, further proving the existence of the pumping effect of the dynamic cone angle [21]. [PERSON] et al. [22; 23] and [PERSON] et al. [24] found the mode shapes of the atomizing sheet under different resonances through simulation and found that the factors affecting the atomization rate were the driving voltage, the driving frequency and cone-hole-related parameters through experiments. Based on the analytical model of the stepped plate, [PERSON] et al. studied and discussed the influence of the geometric shape parameters and mechanical properties of the piezoelectric element, vibration plate, and perforation, so as to achieve the best atomization efficiency of the atomizing sheet [25]. [PERSON] et al. proved through finite element analysis and experiments that the velocity of the metal film on the atomizing sheet and the slope of film displacement across the film length are key parameters affecting the atomization ability, which can be used to improve the velocity and atomization of high viscosity liquid [26]. To sum up, the finite element method is indispensable in simulating the vibration of atomizers when analyzing the factors affecting the atomization performance of dynamic mesh atomizers.