Harmonic Response of a Layered Halfspace Using Reduced Finite Element Model With Perfectly-Matched Layer Boundaries

Abstract

The current paper investigates the use of perfectly-matched layers (PML) as absorbing elements for a finite element (FE) model simulating a semi-infinite medium. This formulation is convenient for application of Craig-Bampton reduction (CBR), which significantly reduce the number active degrees-of-freedom in the model in an attempt to improve the computational efficiency. The results from this investigation suggest the PML elements worked seamlessly with the FE elements to approximate the elastodynamic response of a 2D layered halfspace subjected to a surface load; the wave energy appears to be fully absorbed by the PMLs regardless of incident angle or wavelength. The size of the model is reduced by approximately 77% using the CBR, which transforms the system into a mixed set of coordinates, including both modal and spatial coordinates. The model reduction is accomplished by neglecting modal frequencies for the system above one and a half times the maximum forcing frequency of interest. By only transforming the frequency-independent FE section into modal coordinates, and leaving the frequency-dependent PML elements as spatial degrees-of-freedom, the mode-shapes must only be solved once and can then be reused for different forcing frequencies. The results from this investigation suggest this could provide computational benefits if a number of cases are being computed for different frequencies.