A Study on Edge Wave Propagation in an Incompressible Anisotropic Initially Stressed Plate of Finite Thickness
Date
2025
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Department of Mathematics, NITS
Abstract
This study investigates the propagation of edge waves in an incompressible, anisotropic, initially stressed elastic plate of finite thickness and infinite length. Using Biot’s theory of incremental deformations, a closed-form dispersion relation for edge waves is derived. The analysis accounts for the influence of material anisotropy and initial stress components. Special cases are examined to validate the model against known solutions in stress-free and isotropic conditions. Notably, it is observed that edge waves cannot propagate in a thin isotropic plate without initial stress, whereas in the limit of a thick plate, the solution approaches Rayleigh wave propagation in a half-space. Numerical simulations are performed to explore how the normalized wave velocity c β depends on various physical parameters. The key variables include the normalized initial stress components S11 2Q and S22 2Q , as well as the scaled thickness parameter H = kh, where k is the wave number and h is the plate thickness. Initially, an isotropic case is assumed with N = Q. Results show that increasing S22 2Q leads to a significant reduction in wave velocity, consistent with acoustoelastic effects observed in compressively stressed media. In contrast, variation in S11 2Q causes a more modest reduction in velocity, highlighting the directional sensitivity of the wave response. Further simulations introduce anisotropy by allowing N Q = R to vary, representing different levels of directional stiffness. For fixed H, increasing R influences the dispersion behavior, with distinct shifts in the velocity profile depending on whether the medium is stiffer or more compliant in the transverse direction. Additionally, increasing H generally leads to higher wave velocities in the isotropic case, while in anisotropic media, the trend may reverse, indicating a complex interplay between geometry, pre-stress, and material anisotropy. These findings provide new insights into edge wave dynamics under realistic mate rial and stress conditions and have implications for non-destructive evaluation, micro acoustic device design, and the analysis of wave propagation in pre-stressed elastic structures.