Local Transmitting Boundaries

Abstract

Transmitting boundaries are mathematical artifacts used to prevent wave reflections at the edges (or boundaries) of discrete models for infinite media under dynamic loads. Since the discrete models used are necessarily finite in size, echoes would indeed develop at the artificial boundaries if no appropriate action were taken. A number of these boundaries have been proposed in the past with recourse to various mathematical or physical principles. The present paper is concerned with an analysis of the most common and well‐known of these devices, namely the boundaries of Lysmer‐Kuhlemeyer, Engquist‐Majda, Ang‐Newmark, Smith‐Cundall, and Liao‐Wong. It is shown that they are all mathematically equivalent, and therefore, that they must have comparable wave‐absorbing attributes. Of particular interest is the proof that the Smith‐Cundall boundary (which until recently was believed to be a perfect absorber of waves when multiple reflections cannot occur) has only a limited absorbing capacity. Hence, these various transmitting boundaries are essentially alternative realizations of one and the same boundary mechanism.