**1. Introduction**

The piezoelectric diaphragm pump, which uses a piezoelectric actuator as a drive unit, is a common form of positive displacement pump. This type of pump has the advantages of simple structure, easy miniaturization, zero electromagnetic interference and low noise, so it is widely used in many fields such as biomedicine [1–3], fuel cells [4–6], cooling systems [7–9], and household appliances [10].

A typical piezoelectric diaphragm pump uses a circular piezoelectric vibrator to directly drive fluid. In order to construct a closed volume pump chamber, the vibrator must be sealed to the periphery of the pump body. This installation limits the deformation of the vibrator, making it difficult for the pump chamber to obtain a large volume change. To eliminate the limitations on the structure and installation, researchers have separated the piezoelectric actuator from the diaphragm of the pump chamber to make an indirect drive piezoelectric diaphragm pump [9,11,12]. Meanwhile, the resonance principle is used to amplify the vibration displacement of the piezoelectric actuator to drive the diaphragm—and to increase the volume change of the pump [12]—in order to form a piezoelectric resonance diaphragm pump (hereafter referred to as a piezoelectric resonance pump).

The driving device of the early piezoelectric resonance pump was mainly composed of a piezoelectric stack [5,9,13–15]. It had a large driving force and high precision, but the manufacturing process was complex, with the features of high cost, large volume and high replacement cost if damaged. In recent years we have seen an increase in studies of piezoelectric resonance pumps. These studies mainly used piezoelectric vibrators in different shapes, such as circular, annular and rectangular vibrators, as the driving device of the pump.

In 2012, Jilin University developed a gas piezoelectric resonance pump with a large pump chamber compression ratio, using an annular bimorph piezoelectric vibrator as the driving device [11]. In 2014, for the precise transportation of chemical fuel cells, the University of Science and Technology of China developed a piezoelectric resonance pump with a flexible fluid buffer cavity at the outlet and inlet of the pump chamber. The pump used the rectangular piezoelectric vibrator with free ends as its driving device [16] and used the vibration inertia of the vibrator to drive the movement of the diaphragm in the pump chamber. In 2015, the University of Science and Technology of China also designed a piezoelectric resonance pump with double pump chamber units [17]. It consisted of a U-shaped piezoelectric actuator and two diaphragm pump chamber units that were symmetrically arranged. The U-shaped actuator had very good displacement driving capability in the resonant state. In 2016, National Taiwan University developed a split-type piezoelectric resonance pump used in the medical industry [1]. The circular bimorph piezoelectric vibrator drove the diaphragm through the middle strut. The pump chamber unit could be freely disassembled and replaced, reducing the cost of disposals.

Piezoelectric actuators can be divided into several types according to their structures, such as unimorph/bimorph piezoelectric vibrators [10,11], piezoelectric stacks [5], cylindrical piezoelectric actuators [18], cymbal-shaped piezoelectric actuators [19] and so on. These piezoelectric actuators are based on the strain induced in the longitudinal or transverse directions. The unimorph/bimorph piezoelectric vibrator has the characteristics of simple structure, low cost and various forms. Specifically, the annular and the circular piezoelectric vibrators mainly adopt a periphery fixed installation method, which suits a compact piezoelectric resonance pump system [20]. In contrast, the rectangular piezoelectric vibrator is more flexible in installation. For example, it can be fixed at both ends, at one end, or with both free ends. This method is suitable for a piezoelectric resonance pump system with a large displacement output [12]. After analyzing the advantages and characteristics of common piezoelectric vibrators, a square vibrator with a flexible support is proposed in this paper. The vibrator's substrate adopts a hollow design, with only four corners fixed, to form the flexible support. This structure can reduce the constraint of the support method on the vibration of the square vibrator, thereby improving the vibrator's performance on the displacement output. In this study, the abovementioned piezoelectric vibrator was used as the driving device to construct the piezoelectric resonance pump. We also analyzed and calculated a dynamic model of the pump's vibration and conducted experimental research on the prototype.

#### **2. Development of the Piezoelectric Resonance Pump**
