Reflection and transmission of ultrasonic waves in a layered structure with a functionally graded porous piezoelectric base

Abstract

Abstract The phenomenon of reflection and transmission of waves offers valuable insights into the internal composition and structural characteristics of materials. This study investigates the reflection and transmission of waves in functionally graded porous piezoelectric materials. These materials, distinguished by their customised electromechanical attributes and gradual property variations, present a promising avenue for optimizing performance across diverse applications, including ultrasonics. The reflection and transmission of ultrasonic waves in a novel structure, consisting of a fluid half-space (FHS) positioned above n porous piezoelectric layers, situated on top of a functionally graded porous piezoelectric half-space (FGPPHS) is studied in this paper. The material properties of FGPPHS are considered to vary along the vertical direction and and resulting equations are solved analytically and numerically. The transfer matrix method is employed to analytically determine the energy ratios and amplitude ratios for reflected and transmitted waves. Numerical computations are performed to study the impacts of frequency, gradation, angle of incidence, and porosity on the energy ratios. Furthermore, the influence of stacking of the number of porous piezoelectric layers above FGPPHS, and the choice of materials (Barium Titanate (BaTiO 3), PZT − 5H, PZT − 7H) in layers and half-space, on the energy ratios are studied. The absolute value of acoustic impedance is plotted for various angles of incidence and porosities. From the graph, it is found that the acoustic impedance can be controlled by adjusting porosity in the structure. This will be helpful in minimizing the energy loss at ceramic-medium interface and improving the mismatch of acoustic impedances at the interfaces of medical ultrasonic imaging devices or underwater sonar detectors, and NDE applications. Further, because of lower acoustic impedance, lower density and stiffness of porous piezoelectric materials, the outcomes of this study will be helpful in designing SAW devices.