Orthogonal polynomial methods for modeling elastodynamic wave propagation in elastic, piezoelectric and magneto-electro-elastic composites—A review

SH-Wave Propagation in Functionally Graded Magneto-Electro-Elastic Substrate at Irregular Boundaries

“…Vinyas [19] covered the computational analysis of intelligent magneto-electro-elastic materials and structures. To represent the propagation of elastodynamic waves in composites made of elastic, piezoelectric, and magnetoelectro-elastic materials, Othmani et al [20] used orthogonal polynomial methods. In a magneto-electro-elastic layered structure with such a non-perfect and locally perturbed interface, Chaki and Bravo-Castillero [21] investigated the statistical modeling of anti-plane surface waves.…”

Trade-off between ordinary differential equation and Legendre polynomial methods to study guided modes in angle-ply laminate

“…However, when pushed toward modelling the dissimilarities of the multilayer material properties, computations that are reliable require methods that are more accurate. Some comprehensive assessments on this point have become available, such as the work of Yu et al [5] and the review paper by Othmani et al [6]. Specifically, Legendre polynomials can deal with laminate plates only when the elastic properties of multilayers do not change significantly [5,6].…”

Double Legendre polynomial quadrature-free method for axisymmetric vibration of functionally graded piezoelectric circular plates

“…Then, Elmaimouni et al (2005) applied the polynomial method for wave propagation in an infinite homogeneous anisotropic cylinder rod. From then on, orthogonal polynomial method has a wide range of development in terms of wave propagation (Othmani et al, 2022), such as lamb waves in piezoelectric-semiconductor sandwich plates (Othmani et al, 2017), the propagation characteristic of guided waves in FGM plates (Gao et al, 2019), lamb wave propagation in anisotropic composite lamina (Liu et al, 2020a), lamb and SH waves in multilayered PZT-4/PZT-5A composites (Othmani et al, 2020), the reflection behaviors of elastic waves in the FGP microstructures (Liu et al, 2020b),circumferential guided waves in a fractional Kelvin–Voigt viscoelastic FGM hollow cylinder (Zhang et al, 2021a), circumferential guided waves in the anisotropic multilayer composite cylinders (Zheng et al, 2021b), and lamb waves for thermoelastic multilayered plates (Yu et al, 2022). In 2011, Elmaimouni et al (2011) extended the mapping of orthogonal function method into a double Legendre orthogonal polynomial method (DLOPM) to solve the piezoelectric disc resonator, and obtained the normalized frequencies and electric input admittance.…”