Chapter 21 Equipartition of Modal Energy in a Stiff Vibrating String Due to a Finite Curved Boundary Obstacle

摘要

We study the characteristics of stiff strings vibrating against a curved boundary obstacle which is a situation encountered in stringed musical instruments like sitar, veena and tanpura. The wrapping and unwrapping of the string over the curved obstacle introduces a moving boundary which upon appropriate spatial scaling reveals the resulting nonlinearity. We find dominant quadratic nonlinearities which facilitate modal interactions leading to mode-locked solutions in the absence of damping. The analytical results for the phase-locked solutions are obtained using the method of multiple scales (MMS). We have further found a mode-locked state which tends to an equipartition of energy among the various vibrational modes with an increase in the number of modes considered for the analysis....