A theoretical analysis is made for two kinds of noise reduction methods of timing belts. The methods are confirmed experimentally in a companion paper [1]. Modeling the traveling belt as a string with parametric excitation in tension and density, we obtain an approximate solution for the amplitude of the transverse vibration and carry out some numerical computations for the response of the belt. It is shown that the maximum amplitude of the transverse vibration at resonance is reduced by the two kinds of parametric excitation. The method of variable tension suppresses the maximum amplitude almost for all modes of vibration at resonance and that of the variable density is effective for higher modes except the first mode at resonance.

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