Nonlinear oscillations of a current-carrying string in a magnetic field

A. K. Tomilin ; I. S. Konovalenko ; I. S. Konovalenko

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 163-174

Résumé

The nonlinear properties of a string must be taken into account when creating string systems that are used in transducers and musical instruments. The forced oscillations of an electrically conductive string in a magnetic field are described by a nonlinear integro-differential equation. The amplitude-frequency characteristics of nonlinear resonances of the first and second orders are obtained. The damping factor of the first-mode oscillations is determined from the optimal coincidence of the experimental and theoretical amplitude-frequency characteristic graphs. The experimental amplitude-frequency characteristics for the first-order resonance is obtained using a laboratory setup with a copper string 0.4 mm in diameter and 0.57 m long, having a certain initial tension. The cumulative damping factor of the first mode is obtained, which takes into account all the dissipative factors of a real string system. Low-frequency thermoparametric oscillations of the second mode are observed in experiments with a string. It follows from the analysis of the Mathieu equation that parametric resonance arises even at very low amplitudes of the thermal tension of a string, and it must be taken into account in the frequency analysis of oscillations of string systems.

Détail

Keywords: vibrating string transducers, magnetic force, parametric resonance.