Plotting Lamb Wave Dispersion Curves for Plates

To obtain Lamb wave dispersion curves for plate structures, one needs to compute and visualize the dispersion relationship using the material's longitudinal and transverse wave velocities. The dispersion curve illustrates the fundamental relationship between wave vector (or frequency) and phase velocity, which is critical for understanding wave propagation characteristics in plate-like structures. Implementation typically involves solving the Rayleigh-Lamb frequency equations through numerical root-finding algorithms such as the bisection method or Newton-Raphson iteration. Key computational steps include defining the frequency range, calculating symmetric and antisymmetric mode solutions, and handling numerical instabilities near cut-off frequencies. Analyzing these curves enables determination of material anisotropy, wave mode separation, and dispersion properties essential for non-destructive testing and structural health monitoring applications in aerospace and civil engineering.