Abstract
This paper deals with dynamic response of a ring foundation subjected to propagating seismic waves. The ring foundation is assumed to rest directly on semi-infinite elastic medium. The displacement function of the soil is evaluated by the application of Nakano's solution derived from the three-dimensional wave equation (5). Numerical results are examined in the range of low frequency by Tajimi's approximate method (1). The stresses and displacements in the ring are calculated by solving the boundary condition in frequency domain. The result of numerical examples is summarized as the followings. 1) For higher circumferential mode numbers, namely n=2, the tendency to inextensional deformation of ring is ascertained. And the magnitude of the radial displacement of ring is nearly equal to the radial displacement of the input waves, when the radial displacement of the input waves is larger than the circumferential displacement. 2) In the range of low frequency where the displacement component of seismic waves is large, the axial stress in the circumferential direction of n=0 and the bending stress of n=2 are predominant among the other stress components. 3) The effects of the width ratio to the diameter of the ring are compared with two cases; 0.1 and 0.2. In case of 0.2, the axial stresses of n=0 and 1 are less, but the bending stresses of n=2 and 3 become larger than that of 0.1, respectively. 4) In order to analyze the ring foundation of this problem, a static method is not adequate in the high frequency range, and the dynamic method proposed here should be used.
