Wave Propagation in Functionally Graded Materials

Functionally graded materials (FGMs) exhibit continuous spatial variation in composition and microstructure, yielding tailored gradients in density, elastic moduli and other physical properties. This inhomogeneity profoundly influences the behaviour of acoustic and elastic waves, from bulk longitudinal and transverse modes to guided waves such as Lamb and Rayleigh waves. The continuous gradation alters local stiffness and inertia, leading to non-uniform dispersion, mode conversion and complex attenuation phenomena. In plates, shells and layered structures, gradation profiles can be engineered to control phase velocity, confine energy or attenuate unwanted modes, offering avenues for enhanced non-destructive evaluation, vibration damping and acoustic filtering. Theoretical treatments draw on polynomial expansion, transfer-matrix and shear-deformation theories to capture graded effects across various geometries, while numerical methods such as finite-element analysis support detailed design studies. Recent advances have extended the analysis to viscoelastic, piezoelectric and quasicrystalline FGMs, elucidating coupled field interactions and transient dynamics. These insights have accelerated the deployment of FGMs in aerospace components, high-temperature pipelines, ultrasonic sensors and energy-harvesting devices, underlining their global significance in advanced manufacturing and structural health monitoring.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Research from all publishers

Recent studies have elucidated Lamb wave behaviour in FGM sandwich plates, employing a volume-fraction curve coupled with Legendre polynomial expansions to derive dispersion relations without slicing the plate into discrete layers. Numerical and finite-element simulations validate the theoretical dispersion curves and demonstrate how gradient functions modulate both symmetric and antisymmetric modes, offering guidance for acoustic sensors in monitoring layered composites. Parallel work on viscoelastic functionally graded cylindrical shells, based on first-order shear deformation theory and a Kelvin-Voigt model, has produced analytical expressions for longitudinal guided waves. The phase velocity and attenuation of primary modes are shown to depend sensitively on gradient patterns, viscoelastic parameters and geometric ratios, informing the design of damping elements and ultrasonic devices. Complementing these frequency-domain analyses, investigations into transient wave propagation in viscoelastic FGMs have considered non-stationary longitudinal waves in infinite layers and hollow cylinders. By approximating continuous grading with multiple homogeneous sub-layers, the dynamics of pulse propagation and the influence of viscosity and inhomogeneity on wave fronts have been characterised, supporting real-time structural health monitoring under dynamic loads.

Wave Propagation in Functionally Graded Materials publication trend

The graph below shows the total number of articles in wave propagation in functionally graded materials across all publications each year (not limited to Nature Index journals).

Technical terms

Functionally graded material: A composite with spatially varying composition and properties designed to achieve specific performance gradients.

Lamb waves: Guided elastic waves in plates featuring symmetric and antisymmetric modes arising from boundary interactions.

Dispersion curve: A plot of wave frequency versus phase velocity or wavenumber, showing how propagation speed varies with frequency.

Phase velocity: The speed at which a wave phase propagates along a medium, distinct from group velocity.

Attenuation coefficient: A measure of the exponential decay of wave amplitude per unit distance due to material damping or scattering.

Viscoelasticity: Material behaviour combining elastic response with time-dependent viscous dissipation.

References

1. Lamb Waves Propagation Characteristics in Functionally Graded Sandwich Plates. Sensors (2022).
2. Wave Propagation in the Viscoelastic Functionally Graded Cylindrical Shell Based on the First-Order Shear Deformation Theory. Materials (2023).
3. Transient Wave Propagation in Functionally Graded Viscoelastic Structures. Mathematics (2022).
4. Rayleigh Waves Propagating in the Functionally Graded One-Dimensional Hexagonal Quasicrystal Half-Space. Crystals (2023).