Transverse Wave Propagation in Functionally Graded Structures Using Finite Elements with Perfectly Matched Layers and Infinite Element Coupling

Kulandhaivel Hemalatha, Anandakrishnan Akshaya, Ali Qabur, Santosh Kumar, Mohammed Tharwan, Ali Alnujaie and Ayman Alneamy ()
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Kulandhaivel Hemalatha: Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
Anandakrishnan Akshaya: Department of Mathematics, Rajalakshmi Engineering College, Thandalam, Chennai 602105, India
Ali Qabur: Department of Civil and Agricultural Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia
Santosh Kumar: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, India
Mohammed Tharwan: Department of Mechanical Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia
Ali Alnujaie: Department of Mechanical Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia
Ayman Alneamy: Department of Mechanical Engineering, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2025, vol. 13, issue 13, 1-20

Abstract: This study investigates the propagation of shear horizontal transverse waves in a functionally graded piezoelectric half-space (FGPHS), where the material properties vary linearly and quadratically. The analysis focuses on deriving and understanding the dispersion characteristics of such waves in in-homogeneous media. The WKB approximation method is employed to obtain the dispersion relation analytically, considering the smooth variation of material properties. To validate and study the wave behavior numerically, two advanced techniques were utilized: the Semi-Analytical Finite Element with Perfectly Matched Layer (SAFE-PML) and the Semi-Analytical Infinite Element (SAIFE) method incorporating a (1/ r ) decay model to simulate infinite media. The numerical implementation uses the Rayleigh–Ritz method to discretize the wave equation, and Gauss 3-point quadrature is applied for efficient numerical integration. The dispersion curves are plotted to illustrate the wave behavior in the graded piezoelectric medium. The results from SAFE-PML and SAIFE are in excellent agreement, indicating that these techniques effectively model the shear horizontal transverse wave propagation in such structures. This study also demonstrates that combining finite and infinite element approaches provides accurate and reliable simulation of wave phenomena in functionally graded piezoelectric materials, which has applications in sensors, actuators, and non-destructive testing.

Keywords: semi-analytical FM; FGM; transverse wave; Wentzel–Kramers–Brillouin; gradedness parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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