Calculating the full leaky Lamb wave spectrum with exact fluid interaction.

Area of Science:

• * Solid Mechanics
• * Acoustics
• * Wave Propagation

Background:

• * Lamb waves are elastodynamic guided waves essential for non-destructive evaluation (NDE), sensors, and material characterization.
• * Accurate knowledge of frequency-dependent wavenumbers (dispersion characteristics) is critical for these applications.
• * Fluid-plate interaction introduces a nonlinear differential eigenvalue problem with energy exchange mechanisms like acoustic radiation.

Purpose of the Study:

• * To develop a robust numerical method for solving the differential eigenvalue problem arising from fluid-plate interactions.
• * To accurately determine the dispersion characteristics (phase velocity and attenuation) of leaky Lamb waves.
• * To provide a reliable alternative to traditional, numerically ill-conditioned root-finding methods.

Main Methods:

• * Application of a spectral collocation scheme to discretize the governing differential eigenvalue problem.
• * Transformation of the problem into an equivalent fourth-order polynomial eigenvalue problem, linear in state-space.
• * Utilizing modern numerical methods for solving the transformed eigenvalue problem.

Main Results:

• * The proposed method successfully finds all relevant Lamb wave modes, including those with complex wavenumbers.
• * Generated phase velocity dispersion and attenuation curves show excellent agreement with existing analytical and perturbation methods.
• * The approach effectively handles energy exchange via acoustic radiation.

Conclusions:

• * The spectral collocation method offers a numerically stable and comprehensive approach to leaky Lamb wave analysis.
• * This technique is applicable to a wide range of plate configurations, including anisotropic, viscoelastic, inhomogeneous, and layered structures.
• * The findings advance the capabilities for precise material characterization and NDE using guided ultrasonic waves.