Analytical computation of the dominant dispersion trend of Lamb waves in plate-like structures with an improved dynamic stiffness matrix method

Lamb waves have infinite number dispersion modes; however, no every mode is excitable and detectable. Traditional matrix methods can calculate the dispersion curve of each mode over the full range of possible frequencies. However, the resulting numerically calculated multimodal dispersion curves do not fully represent the dispersion curves measured in real experiments, which are most often dominated by energy from specific modes. An improved dynamic stiffness matrix method is proposed herein to overcome such challenges of the traditional matrix methods. The first step of the improved method is to calculate the displacement response of a plate-like structure under a vertical dynamic loading using the global stiffness matrix of the structure, then the dominant dispersion trend is extracted from the displacement using the phase-velocity scanning scheme. The improved method is verified with three case studies representing typical plate-like structures in structural engineering. The results demonstrate that dispersion trends calculated with the improved method have good agreement with those obtained from experimental measurements.