# Modelling and Study of the Effect of Geometrical Parameters of Piezoelectric Plate and Stack
###### Abstract  
The piezoelectric stack is employed as an actuator and a sensor in a variety of technical applications. The dynamic modelling of piezoelectric plates and stack is used to investigate and search for new applications in mechatronics systems that are based on various loading frequencies. Stacks are composed of series of the same size and whose plates feature the same material properties and are layered by dielectric sheets. This enables increased displacements to be achieved while freeing up more space. The major aim of this study was to investigate the feasibility of using differently modulated piezoelectric plates in a single stack. Mathematical modelling and the study of the characteristics of piezoelectric plates, as well as the stack, with respect to various geometrical parameters, enhances the utilization of the plate in mechatronics systems. The work focuses on the ability of piezoelectric stacks to generate complex vibration spectra comprising numerous frequencies. This is accomplished by utilizing different piezoelectric plates in the stack or by stimulating each plate with a distinct carrier frequency. The plate responses at a wide frequency of piezoelectric plates were investigated using several modeling environments and, finally, experimental findings were obtained. In addition to generating the hypothesis of triggering the plate in a single stack with a varied frequency spectrum, the experiment performed was employed for parameter identification. The experiment demonstrated that it is possible to increase the flexibility of systems by employing piezoelectric stacks as a mode of actuation and that piezo stacks can be used in systems that require precise actuation over a wide frequency range. piezoelectric plate; frequency spectrum; piezoelectric stack; geometric parameters +
Footnote †: journal: Applied Sciences  
10 October 2021  
17 December 2021  
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**1. Introduction**  
Piezoelectric materials are a type of smart material that may be employed as sensors (when a load is applied, it generates voltage) and actuators (when voltage applied it deforms). The intimate interaction of piezoelectric actuators and sensors in structural vibration attenuation makes the material distinct and smart. Piezoelectricity is the potential of a substance to produce electrical charges in response to mechanical strain. The opposite effect, deformation under the influence of an external electric field, is called the inverse piezoelectric effect. The direct effect enables piezoelectric materials to be used as sensors, and the converse effect enables them to be used as actuators. Piezoelectric ceramics, particularly lead-zirconate-titanate (PZT) variants, are the most commonly used piezoelectric materials. Piezoelectric materials have been used to actively suppress the vibration of civil structures, minimize the vibration of helicopter rotor blades, actively regulate the aero-elastic flutter of aircraft, and actively control the vibration of hard disk drives [1, 2, 3]. The most common benefits of piezoelectric stacks are vibration attenuation, energy harvesting and linear micro/nano manipulation [4, 5]. Essentially, several passive and active vibration damping strategies are commonly used to attenuate structural vibration. The suppression of vibration at vibration sources, during propagation and dissipation of vibration energy was a subcategory of passive damping methods [6, 7]. Active vibration damping methods used the additional energy system to dampen unwanted vibration bygenerating interference vibration patterns that cancel unwanted coming vibrations [8]. The superior dynamics of electrical actuators, particularly when using the piezoelectric theory, allow new fields of operation for noise and vibration control. The avoidance of noise and vibration is a significant challenge in the construction of helicopters and combustion engines [9].