Transmitting boundary

J.M. McGlaun, Improvements in CSQII A Transmitting Boundary Condition, SAND82-1248, Sandia National Laboratories, Albuquerque, NM, 87185, 1982. 

The modes of vibration in a cylindrical coordinate system can be obtained through the method of separation of variables (Kausel 1974 Tassoulas 1981). Using the modes of vibration, equivalent nodal loads and nodal displacements can be evaluated at the cylindrical boundary r= ro of the region r>ro and the dynamic stiffness of the transmitting boundary in the water-saturated transversely isotropic layered strata can be obtained. The amplitudes of the equivalent nodal loads are given as follows ... 

The far-field region of the water-saturated transversely isotropic ground in a cylindrical coordinate system can be represented by this transmitting boundary. 

The earthquake response, as a direct time-domain representation, of the cylindrical liquid storage tank installed in the water-saturated transversely isotropic soil strata can be obtained by employing the numerical models of the cyHndrical tank structure, the stored liquid, the near-field region of the ground, and the transmitting boundary. The equations of motion for the tank structure, the stored Hquid, and the near-field region of the ground can be written in the time domain as follows ... 

Kim, J.K., Koh, H.M., Kwon, K.J. Yi, J.S. 2000. A three-dimensional transmitting boundary formulated in Cartesian co-ordinate system for the dynamics of non-axisymmetric foundations. Earthquake Engineering and Structural Dynamics 29 1527-1546. 

Lee, J.H. 2007. 3-D Transmitting Boundary in Cylindrical and Cartesian Coordinate Systems for Soil-Structure Interaction Analysis in Water-Saturated Transversely Isotropic Layered Ground. PhD dissertation, Seoul National University, Seoul, Korea (in Korean). 

Lee, J.H. Kim, J.K. 2008. Transmitting boundary for water-saturated transversely isotropic strata based on the u-U formulation. Soil Dyn Earthquake Eng, doi 10.1016/ j.soildyn.2008.08.003. 

In the case of a perforated-wall caisson mounted on a rubble foimdation as in Fig. 13.3, the incident wave height at the perforated wall Hy, is a priori imknown. In the case where the caisson does not exist and the water depth is constant as hs for X > 0, MasseP has shown that the transmitting boundary condition at x = 0... 

Pressure-Transmitting Boundary Conditions for Molecular-Dynamics Simulations. 

Lee MKW, Finn WDL (1978) DESRA-2, dynamic effective stress response analysis of soil deposits with energy transmitting boundary including assessment of liquefaction potential, Soil mechanics series no 38. Department of Civil Engineering, University of British Columbia, Vancouver... 

The impedance for an absorbing or transmitting boundary where concentration of species outside of the diffusion layer at distance X from the electrode surface is constant as C(X >L, t) = C and the species are instantly consumed at the electrode surface as C (X = L, t) = 0 [1, p. 59, 3]. The situation can be represented by negligible charge-transfer impedance where Z j(o) = 0, and Eq. 5-45 becomes [36] ... 

---