Analytical approach on stress analysis in a functionally graded piezoelectric annular disk with varying compressibility and varying density under internal pressure

Abstract

When a crystal is subjected to mechanical stress, it exhibits piezoelectricity, also known as the piezoelectric effect, which is the emergence of an electrical potential across the crystal's sides. A few examples of piezoelectric materials include quartz, Rochelle salt, lead zirconate titanate (PZT4) and zinc oxide (ZnO). Piezoelectricity has many applications in regards to electrical transducers and signal devices. In this paper, the analytical solution is obtained for elastic-plastic stresses in a thin rotating disc formed of functionally graded piezoelectric material with varying compressibility and varying density for distinct angular velocity with internal pressure using Seth's transition theory. The distribution of the mechanical and electrical components can be precisely controlled by applying functionally graded piezoelectric materials (FGPMs). Transition theory assumes that a mid-zone (transition state) exists between elastic state and plastic state. A nonlinear Governing equation of the problem is formulated using equilibrium equation by substituting the values of stresses. For evaluation of transitional stresses, transition function R is assumed in terms of radial stresses and equations are solved analytically by considering the transition (critical points) of the differential equation. The investigation focuses on how the rotational velocity and internal pressure affects the radial and circumferential distribution of stresses. With the help of graphs and mathematical calculations, it is observed that both variable density and variable compressibility have significant effect on the performance of a functionally graded piezoelectric materials. Therefore, it can be concluded that an annular disc made up of functionally graded piezoelectric materials is safer than that of homogeneous piezoelectric materials for engineering design purposes.