| Abstract: | The unfolded cone model used for calculating the dynamic response of a disk on the surface of a soil layer resting on flexible rock for translational motion is extended to rotational motion. The method is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient – α replaces the coefficient of total reflection – 1. The modified value of – α, which, in general, is frequency-dependent, is determined by considering one-dimensional wave propagation along the cone for the first impingement at the layer–rock interface. The low- and high-frequency limits of – α for the rotational motion are the same as for translational motion. As these limits do not depend on frequency, the dynamic analysis using cones can be performed in the familiar time domain. The transfer function constructed by addressing the reflections–refractions at the soil–rock interface and the reflections at the free surface in the unfolded cone model is highly accurate, resulting in the same accuracy of the dynamic response of a disk on a layer resting on flexible rock as that on a homogeneous half-space modelled with a cone. |
