| Abstract: | In foundation dynamics a most important effect, often overlooked, is that for a soil layer on rock a cutoff frequency exists, below which there is no radiation damping. Valuable insights into the nature of the cutoff frequency may be obtained without solving differential equations. Physically motivated wave-propagation techniques enable modification of familiar unbounded cone models to represent layered soil. Echoes corresponding to the natural period of the layer appear to account for the cutoff frequency. The cone models have simple solutions in both the time and frequency domains. An investigation of the simplest system with a cutoff frequency, the shear bar on an elastic foundation, shows that, for radiation to take place, the radius of penetration of waves must extend to infinity. In order to reach infinity, the waves' displacement amplitude must die off in a special way, otherwise conservation of energy would be violated. These considerations reveal a general radiation criterion, namely, that the waves' amplitude must diminish in inverse proportion to the square root of the far-field boundary surface. Using the radiation criterion, it is possible to derive transmitting boundaries for shear waves which replace the far field. |
