An analysis is carried out to investigate the dynamic characteristics of a rotating, thermally loaded circular saw that undergoes tensioning over a double annular domain. By using the plate bending theory, the governing equations for the in-plane behavior during rotation and under thermal load and plastic strain and those for the resulting out-of-plane behavior are derived. Then, the solution of in-plane forces is obtained and the modal analysis is carried out. The in-plane forces and natural

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... equencies are calculated numerically to investigate their dependence on tensioning conditions and to find suitable tensioning conditions for the stable operation of the saw. 1156 and natural frequencies analytically and experimentally (9), (10) ; Schajer and Mote obtained the in-plane stresses and natural frequencies and investigated the effect of the magnitude of roller indentation on the natural frequencies (11) . Mote and Nieh (12) measured the natural frequencies in the tensioned saw, taking into consideration important effects due to rotation-an issue disregarded in the above studies (8)-(11) . Another important aspect of the operation of circular saws is the thermal load on their periphery, resulting from the friction between the blade and the workpiece. Mote and Nieh (13) and Kimura (14) obtained the temperature distribution in a rotating saw undergoing burner heating at its periphery. As mentioned in the above studies (9)-(12) , the natural frequency has a significant impact on the stability of a circular saw: generally, increasing the natural frequency improves stability. Tensioning serves this purpose. Whether or not this is achieved depends on the control of the distribution of the applied plastic deformation, which requires skill and years of experience. In order to improve the efficiency of the tensioning, it is important to determine the field in the tensioned saw in use and investigate its detailed dynamic behavior. As stated earlier, rotation and thermal load are important factors for the performance of the tensioned saw in use. Ishihara et al. (15) , therefore, considered both effects and obtained the natural frequencies of the rotating tensioned saw under a thermal load. In the study (15) , the authors treated the tensioning over a single annular domain as a fundamental study and investigated the effects of tensioning on the in-plane forces and natural frequencies. In reality, however, the tensioning over a multiple annular domain is often introduced aimed at improving the efficiency of tensioning. This paper, therefore, presents a theoretical analysis of the elastic field and the resulting dynamic characteristics of a rotating, thermally loaded circular saw that undergoes tensioning over a double annular domain. The analytical model used is an annular disc that is rotating, subjected to a local temperature distribution assuming the thermal load caused by friction between the blade and the workpiece, and given the in-plane plastic strain introduced by tensioning. On the basis of the plate bending theory, the governing equations for the axisymmetric in-plane behavior due to rotation, thermal load, and plastic strain and for the resulting unsymmetric out-of-plane behavior are derived. Then, the analytical solution for in-plane forces is obtained and the modal analysis of the disc is carried out. Numerical calculations are performed to evaluate the in-plane forces and natural frequencies of the saw, to investigate the effect of varying conditions such as the tensioning strength and location on the in-plane forces and natural frequencies, and to determine suitable tensioning conditions for the stable operation of the saw. 2 , 1 = j denote the corresponding widths of the nonzero