Compatible Viscous Boundary for Discrete Models

A numerical method for dynamic analysis of an infinite discrete model by compatible replacement to a finite discrete one has been devloped. The proposed finite model consists of one-dimensional lumped masses, shear springs, and perfectly absorbing dashpots which are arranged to the boundaries. These compatible viscous boundaries are applicable to any types of waves within the cutoff frequency. Theoretical reflections at the hybrid viscous boundaries proposed by Lysmer are shown and compared with those at the compatible viscous boundaries. Numerical considerations are made on sinusoidal and random vibrations of the finite models. In the proposed compatible model disturbances always travel in the same form independent of the number of masses; however, the hybrid viscous boundaries cause imperfect absorptions which depend on the wave-length of waves and the mesh spacing of the finite model.