Dynamics of simple string subject to unilateral constraint: A model analysis of sawari mechanism

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The sawari is an instrumental mechanism of biwa and shamisen. Its physical structure involves a solid surface of very small size that the vibrating string touches dynamically, creating a peculiar timbre in the produced sound. This paper proposes a model of the sawari mechanism, which is a unilateral constraint on the displacement of a string, that is, a mechanism that is essentially nonlinear and time-dependent because of contact/separation phenomenon. Here, the key point of the model is the repelling force caused by the lateral elastic deformation of the string. The study is focused on the dynamic effect under an idealized problem setting so that the string vibrates at no loss of mechanical energy without any interaction with other objects such as a resonator that terminates the string in the real instrument. A numerical method is given for the computation of this problem. The numerical results show a gradual build-up of high-frequency oscillations that eventually prevail over the entire string motion. The short-term spectrum changes in a continuous way with time, maintaining a nearly harmonic structure on the fundamental frequency of the associated sawari-free problem.

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