Dynamic Equations of Motion of a Flexible Single Block on a Rigid Surface

Prismatic graphite blocks are major components of the reactor core structure of a prismatic type HTGR (High Temperature Gas Cooled Reactor). The vertically stacked prismatic graphite fuel blocks and graphite reflector blocks form a group of graphite block columns. And each column has gaps between neighboring columns and stands on the core bottom structure by itself. An earthquake loading on stacked blocks causes rocking responses and solid impacts between them, and may lead to structural integrity problems. The seismic analysis of a HTGR core structure composed of stacked prismatic graphite blocks has been an important design issue and has a long history. The dynamics of a block as well as stacked blocks are quite complex, and they are not fully understood yet. A basic systematic understanding of the rocking response of a rigid block resting on a rigid floor had not been well established until when G.W. Housner first presented it in 1963. In 1975, T.H. Lee presented a methodology for analyzing the nonlinear response of a column of stacked prismatic fuel blocks. In 1979 T. Ikushima and T. Nakazawa presented their work results on a seismic analysis of a column of stacked prismatic fuel blocks and compared them to the seismic test results of a half scale model. Their numerical model is similar to that of Lee's study, but the parameters in their analysis were from their scaled model tests and the results were verified. A stochastic analysis methodology for a rocking block was introduced by Pol D. Spanos and Aik-Sion Koh; they considered a rocking block on the Winkler foundation. After their works some other researchers have studied new techniques to solve the nonlinearity problems of block impacts on the base. S. J. Hogan considered the dynamics of a slender rigid block mounted on a vibrating rigid table with side walls. The governing equation is quite simple, but it shows complex nonlinear dynamics and gives many types of solutions nevertheless