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We are developing an estimation method of radiation sound from automotive tire in operation by using experimental statistical energy analysis. It is, however, difficult to experimentally verify estimation results of the radiation sound. It is because tire is complicated structure with super-elastic damping and multi-layered materials, and there is no alternative method to measure the radiated sound from the tire. Also, the effect of acceleration of rolling tire is not understood. Then, we are trying to develop a numerical verification method of our method by using a simile rod or beam of which both edges are continuous like a ring, with a moving force. This paper describes the developments of a numerical simulation methods for the rod with continuous boundary and for acceleration effect based on the time-variant beam-forming algorithm. The displacements and energies calculated by these simulation methods were examined for steady and accelerating conditions. As a result, it was found that the acceleration effect is appeared in the frequency domain as the spectrum is overspread through wider frequency range.