An Application of Cellular Automata (CA) to Wave Propagation Problems (1st Report, Local Rules of Flexural Vibration of the Beam)

Abstract

Flexural vibration of the beam is studied using Cellular Automata Method (CA). Local rules of flexural wave propagation are derived analytically. Assuming the initial displacement of the beam to be impulsive wave, deformation pattern of that wave is calculated for progressive wave after one sampling period, and that pattern is considered to be the local rule of the flexural vibration. The deformation pattern is expressed like finite impulse response filter h(x), so convolution of flexural wave along x-axis is calculated at every sampling time. Transfer functions of displacement between two points along the beam are calculated by CA when progressive wave traveling, and are compared with analytical one. Both amplitude and phase are agreed with analytical one. The local rule of reflection at simple support boundary are also derived. Then resonant frequency of the simple support beam are calculated by CA. There are also good agreement between CA and analytical one. The good agreements suggested that the local rules of flexural wave are sufficiently reliable.