Modelling Piezoelectric Vibrations

Abstract

Exploring the vibrational characteristics of various structures, such as radial, breath, thickness-shear, and asymmetric, is essential for acoustics, mechanical engineering, optics, biomedical engineering, and materials science. These modes enable better understanding of the material and structural behaviour under different conditions, which can improve the design, optimisation, and dependability of engineering components. Hook’s law, which is the basis of linear elasticity, is a fundamental concept in engineering, allowing for accurate predictions of solid object deformation under different loads. Developing precise mathematical models and simulations based on linear elasticity principles can further enhance the analysis of material behaviour. Examining free vibrations in different solid objects, such as sapphire cylinders, zinc shells, and piezoelectric structures, provides important insights for designing and optimising devices in various industries. Investigating transversely isotropic cylindrical shells is especially important, presenting both challenges and possibilities for innovation and optimisation in engineering applications. This research project consists of six chapters that investigate different aspects of materials and their characteristics. We examine the fundamental equations of linear elasticity, such as stress-motion, electrostatics, strain-displacement, electric fields, electric potentials, piezoelectric constitutive equations, and Hook’s law, in both spherical and cylindrical settings to gain a better understanding of their principles and applications. Additionally, we studied the use of barium titanate nanoparticles (BTNPs) in cellular activation by ultrasound, with a focus on quantifying the electrical voltage generated by BTNPs under ultrasound exposure. Moreover, we analyse vibration modes and shear stress in ceramic cylinders, using the theory of three-dimensional elasticity to elucidate the vibration characteristics of solid sapphire cylinders and comparing the proposed approach with existing methods. This study examines the free oscillations of cylindrical shells by constructing stressdisplacement correlations for transversely isotropic cylinders and examining motion equations. Furthermore, the stress-displacement relationship for cylindrical shells, the association between electric charge and displacement, and potential electric fields are discussed. The research culminates in the presentation of nondimensional equations and solutions for stress components, as well as frequency equations for a piezoelectric ceramic material (PZT-4). This work provides useful information on the behaviour of materials and vibrations in different geometrical contexts.