# Modelling and Study of the Effect of Geometrical Parameters of Piezoelectric Plate and Stack
###### Abstract
Additionally, the research established the consistency of classical and non-classical methods of displacement response for various geometrical parameters that affect the plate's characteristics. This property is highly beneficial for designing mechatronics system. Inthis study, a novel approach was applied by composing a single stack with varied sizes of piezoelectric plates, modulating at different frequency spectrum, and evaluating the response. This enables users to actively dampen the complicated vibrations of the structure or system. The mathematical description built in this study for piezoelectric analysis combines a lamped parameter approach, a continuous mass approach, and the finite element method. More broadly, lumped parameter modelling entails the development of electrical and mechanical components that behave analogously to the device under consideration under specified conditions. Lumped parameter methods make use of assumptions and approximations to reduce computation time while maintaining high precision as long as the underlying assumptions are fulfilled. This enables the system's response to be simulated and the relative value and trade-offs between many design parameters to be quantified. The model was synthesized in [12] by integrating the mechanical and electrical domains. FEM predicts practical results by discretizing the model into equal finite elements. In this study, the dynamic response of the plate was modeled using ANSYS software over a wide frequency band. The FEM method was used to obtain the thickness effect of the piezoelectric material over a wide frequency spectrum. The aim was to confirm the analytically solved piezoelectric material response through the simulation of finite element results. Dielectric constants are manipulated by either specifying orthotropic dielectric permittivity on the MP command (interpreted as permittivity at constant strain) or specifying terms of an anisotropic permittivity matrix on the TB command [20]. Modal analysis is commonly used to define a structure's dynamic properties in terms of natural frequencies. The motion of a linear system at a resonant frequency is represented by a normal mode of vibration (eigenfrequency). To characterize the thickness effects, three different thicknesses of piezoelectric plate (2 mm, 4 mm, and 8 mm) were used. Each plate's first six modal frequencies were determined, and the harmonic response over the discovered modal frequency was simulated. The analytical and finite element methods provide useful information for the investigation of the influence of geometrical parameters of piezoelectric plates. Damping coefficient and spring constant parameters were estimated from the experimental findings using the simplex algorithm in order to achieve a realistic conclusion. The idea of studying the possibility of using variously modulated and diverse plates in a single stack shown in Figure 1 was accomplished along with the existing challenges and hurdles related to the suggested concept. From both dynamic model simulation and the experimental results, gluing the same piezoelectric plate creates greater displacement than gluing various sizes of piezoelectric plates.