Modeling guided wave propagation in functionally graded plates by state-vector formalism and the Legendre polynomial...

Area of Science:

• Materials Science
• Solid Mechanics
• Wave Propagation

Background:

• Functionally gradient materials (FGMs) exhibit spatially varying material properties.
• Analyzing wave propagation in FGMs is crucial for structural health monitoring and design.
• Existing methods for FGM wave analysis can be computationally intensive.

Purpose of the Study:

• To develop a novel numerical method for analyzing guided wave propagation in FGM plates.
• To efficiently compute dispersion curves and material properties of FGMs.
• To provide theoretical support for nondestructive evaluation of FGM structures.

Main Methods:

• State-vector formalism combined with the Legendre polynomial method.
• Univariate nonlinear regression for optimizing gradient distribution.
• Transformation of the problem into an algebraic eigenvalue problem.

Main Results:

• Accurate and fast computation of dispersion curves, displacement, and stress profiles for FGMs.
• Validation of the method using chrome-ceramic and iron-based alumina FGM plates.
• Demonstration of the influence of gradient variation and Legendre polynomial order on results.

Conclusions:

• The proposed numerical method offers a fast, flexible, and accurate approach for FGM wave propagation analysis.
• The method simplifies the computation of dispersion curves by avoiding complex root-finding algorithms.
• Results provide a basis for nondestructive evaluation and quantitative assessment of FGM structural characteristics.