Analyzing modal behavior of guided waves using high order eigenvalue derivatives

• A novel approach for mode-tracing of wave modes based on the Scaled Boundary Finite Element Method is introduced.
• Wave modes are traced by means of Taylor- and Padé-approximations.
• Eigenvalue derivatives of arbitrary order are derived analytically.
• The approach allows for the identification of critical sections and possible modifications of the solution process.

This paper presents a mode-tracing approach for elastic guided waves based on analytically computed derivatives and includes a study of interesting phenomena in the dispersion curve representation. Numerical simulation is done by means of the Scaled Boundary Finite Element Method (SBFEM). Two approaches are used to identify the characteristics of the resulting wave modes: Taylor approximation and Padé approximation. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches. Remarkable phenomena in potentially critical frequency regions are identified and the tracing approach is adapted to these regions. Additionally, a stabilization of the solution process is suggested.