# Modelling and Study of the Effect of Geometrical Parameters of Piezoelectric Plate and Stack
###### Abstract
Comfort, safety, and sociability of the environment are important drivers of current successful system research programs. Piezoelectric patches were bounded on the structure to act as dampers [10]. The complex vibration produced by actuating the stack consisting of two piezoelectric plates at different frequencies analyzed in this study enables further research into novel applications and methods for attenuating complex vibration using effective controlling systems. A wafer of piezoelectric material sandwiched between two electrodes is the basic component of a piezoelectric stack actuator. The wafer is polarized uniaxially along its thickness before manufacture, and hence exhibits a substantial piezoelectric effect exclusively in this direction of polarization. A typical piezoelectric stack actuator is made by mechanically joining many wafer parts in series and electrically connecting the electrodes so that the wafers are in parallel. The correlation between the forces applied and the subsequent reaction of the piezoelectric material depends on a variety of parameters, such as the piezoelectric properties of the material, its size and shape, and the direction in which forces, or electrical fields, are applied relative to the axis of the material [8]. Mechanical quantities, such as stress or strain, as well as electrical values, such as electric field, electric displacement (flux density), or polarization, are connected in crystals with piezoelectric characteristics. This is referred to as electromechanical coupling. When a force is applied to a piezoelectric material, the dielectric displacement induces a surface charge, resulting in the formation of an electric field. This field can be accessed as an electric voltage on attached electrodes [11]. A single layer of piezoceramics is not capable of generating sufficient displacement for a satisfactory input voltage. To achieve higher displacement, a thicker plate, as well as an amplified electric field, is required. This issue can be fixed by stacking the plates' layers together. Stack actuators consist of multiple layers of piezoceramics partitioned by electrodes. The layers are polarized around their thickness and axes of motion, so the strain of the piezoelectric material is dependent on the steady load of the axis [12; 13]. Hundreds of individual piezoelectric layers separated by thin electrodes can be considered to compose the stack. Electrically, these layers are connected in parallel, allowing a lower voltage level to generate the necessary electric field. They are mechanically connected in a series configuration, which means that the elongation of each layer contributes to a greater displacement than a single element would. Stack actuators can be divided, according to the input voltage, into low-voltage and high-voltage actuators [14]. The direct piezoelectric effect is appropriate for sensing applications. The usage of piezoelectric sensors in various studies was mostly for noise sensors, in which the vibration of sound at a given frequency is transformed into electrical impulses. Piezoelectric sensors outperform strain gauges in terms of signal-to-noise ratio and high-frequency noise rejection. Piezoelectric sensors are thus well suited for applications involving the measurement of low strain levels. They are small and easy to embed and require only a small amount of signal conditioning circuitry [15; 16]. When geometric parameter findings of piezoelectric plates are performed, it is obvious that the maximum vibration amplitude (power generated) is highly reliant on the resonant frequency of the dominant mode, and the natural frequency changes when the geometry is modified. The influence of thickness, length, and width of the cantilever beam on the maximum resonant frequency was investigated in [17; 18]. In [19], the response of piezoelectric materials with varying parameters was investigated using both classical and non-classical modelling approaches. The purpose of the research was to enhance the plate's displacement by examining various mechanical qualities.