# Modelling and Study of the Effect of Geometrical Parameters of Piezoelectric Plate and Stack
## 5 Conclusions  
In this study, the characteristics of a piezoelectric plate and a stack of two connected plates were investigated and addressed in relation to experimental results. The study aims were to investigate the response of a piezo ceramic plate across a wide frequency range, employing a theoretical, finite element modelling approach, and then to produce a model-based design for the experimental findings. The applications of piezoelectric ceramics are growing and studying more about the characteristics and responsiveness of the plate helps to improve the intelligence of mechatronics systems. The accurate modelling of piezoelectric materials is very useful for developing material properties and proper plate utilization in the system. The dynamic modelling and testing of piezoelectric materials are a challenging problem due to the wide range of phenomena that occur in them, particularly the electromechanical properties of the plate, which currently require significant mathematical computation. In terms of selecting piezo plates based on their physical and geometrical shape for certain MEMS (microelectron mechanical system) applications, mathematical modelling is highly beneficial for addressing the properties of the plate at different parameters. This study attempted to study the geometrical parameter impacts of piezoceramics while taking both electrical and mechanical properties into account. Various FEM packages that provide links with MEMS have emerged recently; in this study, ANSYS Multiphysics was applied. It provides very good findings for the dynamic response of plates with varied geometrical parameters. The well-known approach to increasing plate displacement was to glue a series of piezo plates in the form of a stack. However, attaching a sequence of plates layer by layer increases the volume and space, which may have an effect in some MEMS applications. This disadvantage is also considered in this study in order to investigate how to remedy the problem without affecting the displacement produced. Using lumped parameter approaches, a stack of two plates was synthesized in the form of a cascade model (representation of two piezo plates glued together). The experiment was carried out for the suggested synthesis model and was notably used in this study for parameter identification and validation of the model. The two plates were employed at different geometries and actuation frequencies. The study's goal was to analyze the complicated vibration created by actuating each plate at various frequencies in order to use them in active noise cancellation. Some key results were obtained from the plate dynamic model. Based on the geometry of the plate, the effectiveness of the material's response was explored over a large frequency range. The plate's thickness determines its sensitivity, while its area dictates its deformation. Figure 12: Time domain comparison of piezo stack actuated at frequency of 8 kHz for the lower and 10 kHz for the upper plate. The thicker the plate, the more sensitive the material is to low-frequency response; and the larger the area, the more displacement produced. This is due to the fact that a wider area of the piezo plate's electrode surface is exposed to a higher excitation voltage than a smaller region. The lamped parameter approach used to simulate the dynamic response of the synthesized cascade model agreed completely with the experimental results. The major purpose of modeling the cascade model was to investigate the possibility of modulating the plates in a single stack at different frequencies and generating complicated vibrations. For this study, the stack was made from various plate sizes and materials. Based on both experimental and computational findings, the same piezo plate yields greater displacement than different sizes of plates glued together. The model of piezo plates in this study was primarily planned for use in structural vibration attenuation.