Computation of dispersion curves for embedded waveguides using a dashpot boundary condition

Area of Science:

• Solid mechanics
• Computational physics
• Waveguide theory

Background:

• Calculating dispersion curves for solid waveguides is crucial for understanding wave propagation.
• Previous methods often require extensive computational resources, especially when coupled to infinite media.
• The scaled boundary finite element method (SBFEM) has shown promise for waveguide analysis.

Purpose of the Study:

• To present a novel numerical approach for computing dispersion curves of solid waveguides coupled to an infinite medium.
• To adapt the scaled boundary finite element method (SBFEM) for waveguides interacting with a surrounding medium.
• To demonstrate the computational efficiency of the proposed method.

Main Methods:

• The study employs the scaled boundary finite element method (SBFEM).
• A dashpot boundary condition is introduced at the waveguide-medium interface, utilizing acoustic impedances.
• No discretization of the surrounding infinite medium is required.

Main Results:

• The proposed dashpot approach effectively models the influence of the surrounding infinite medium.
• The number of degrees of freedom is significantly reduced (10-50x) compared to absorbing region methods.
• A substantial reduction in degrees of freedom (up to 4000x) is achieved compared to other finite element methods.

Conclusions:

• The SBFEM with a dashpot boundary condition offers a highly efficient numerical solution for waveguide dispersion analysis.
• This method drastically reduces computational cost without sacrificing accuracy.
• The approach is particularly advantageous for waveguides coupled to infinite acoustic or elastic media.