Study of parametric excitation of nonlinear vibrations in strings

Abstract

The vibration of a string apparatus can easily be modified to demonstrate and study the parametric excitation of nonlinear acoustic vibrations. As faculty at Brown University were pioneers in both the study of nonlinear acoustic phenomena and introducing clever teaching apparatus to illustrate the principles of this science, it seems fitting to present the results of our study in this special session. The direct drive inductive transducer generates an alternating force, which drives a fixed-free aluminum thin beam that is tuned at resonance with the addition of mass. The string is attached to the free end of the beam and a dual pulley system and micro-positioning rail allows for the continuous adjustment of tension. The orientation of longitudinal vibrations in the string modulates the tension and excites transverse resonance modes that match the condition of half the drive frequency. The classic results of highly bent tuning curves are illustrated in this system by adjusting the tension (sound speed) in the string such that the resonance versus wave number spectra can be observed. Thus such a system may be useful in introducing the student to the study of parametric excitation of nonlinear vibrations in simple systems.