Reflection and transmission phenomenon of ultrasonic waves in a layered structure of functionally graded porous piezoelectric material

Abstract In this paper, the reflection and transmission characteristics of ultrasonic waves in a structure composed of a fluid half-space lying over functionally graded porous piezoelectric (FGPP) layers resting on the FGPP base are studied. Functionally graded porous piezoelectric materials (FGPPMs) provide a potential way to optimize performance in a variety of applications, including ultrasonics. They stand out for their customized electromechanical features and progressive property fluctuations. The material parameters of FGPPMs are assumed to change along the thickness direction. The transfer matrix is determined for the FGPP layers. The amplitude and energy ratios have been determined analytically. Numerical computation has been done to assess the effect of the angle of incidence, porosity, frequency, and gradation on reflected and transmitted energy ratios. In addition, the influence of selecting materials such as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>BaTiO</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi>PZT</mml:mi> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi>PZT</mml:mi> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> </mml:mrow> </mml:math> for the FGPP layers on the energy ratio curves is also demonstrated. The graphical analysis has examined the impact of the number of FGPP layers positioned above the half-space. The variation of the acoustic impedance for various porosities is also plotted. The graph indicates that the porosity in the structure may be changed to regulate the acoustic impedance. This will assist in reducing the energy loss at the ceramic medium interface and useful in underwater sonar detectors and medical ultrasonic imaging equipment, as well as non-destructive evaluation applications.