B212 セルオートマトンによるクラドゥニの図形の生成(粒状体関連)

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Recently, Cellular Automata has been rapidly developed and widely used for analyzing many complex problems. In this paper, the phenomena that the sand grain which is initially and randomly spread on the surface of a square plate will crowd around some positions to generate shape of nodal line at natural modes is simulated by using Cellular Automata. Two moving patterns of sand grain are presented, one is the rolling of sand grain at micro-vibration condition or no-vibration position, and another is jump of sand grain at violent vibration or natural vibration condition. The former obeys usual Moore neighborhood rule, and the latter is defined that the jump distance is proportional to the initial vibrant velocity of plate in two directions of plate plane. The calculated procedures are list as following : first, a plate plane is divided into some uniformed grids in which the height of sand grain is defined as a state variable to be discussed in this paper ; then the height of sand grain caused its rolling movement is calculated ; finally, according to above-mentioned rules the height change of sand grain due to jump movement is calculated. The periodic boundary condition is used in simulation. The simple-supported condition at four boundary sides of the plate is mainly analyzed in this paper. In this case, the function of vibrant mode is directly used, and the mode shape is first shown ; then the Chladni's Figure which describes the distribution of sand grain in the plate surface is calculated by CA. Finally, using the same rule to simulate other constrained plates, such as free-boundary-condition and fix-boundary-condition. Two calculated results at mode order M=N=2 are shown in this paper. Due to the periodic boundary condition, sand grain will stack at four boundaries. But useful stacked shape should be observed in central wide area of plate. From calculated results of height distribution figures (Chladni's Figure) of sand grain in different constrained boundaries and mode situations, the nodal line at natural mode condition is clearly seen. Finally, the fact that CA is a useful method to describe the vibration mode is evidenced.
一般社団法人日本機械学会の論文
2001-11-14

B212 セルオートマトンによるクラドゥニの図形の生成(粒状体関連)

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