Vibration of the String with Nonlinear Contact Condition

Abstract

We investigate the vibrations of the ideal flexible string, which one end is rigidly clamped, or coupled with a linear damped oscillator, and another one is terminated on the curved contact surface. The vibrating string touches repeatedly this termination, and this, in turn, causes the modulation of fundamental frequency of the string, and the train of high frequency oscillations is generated. The problem is studied both analytically, and numerically. The effect of the contact nonlinearity and of the shape of the contact surface on of the spectral structure of the string vibration is considered. The influence of the impact amplitude on the vibration spectra of struck string is discussed.