TORUS DOUBLING AND CHAOTIC STRING VIBRATIONS - EXPERIMENTAL RESULTS

Non-linear and chaotic vibrations are well documented in mechanical systems; however, to the best of our knowledge (and somewhat to our surprise) chaotic oscillations have not previously been noted in experimental studies of string vibrations. Two recent theoretical studies predict periodic, quasi-periodic, and chaotic vibrations when strings are subject to large forcing amplitudes. In particular, Johnson and Baja illustrated a torus doubling transition to chaos in a single-mode model (coupled Duffing oscillators) of a linear-elastic string. In this letter we describe a simple experiment that illustrates this torus doubling transition to chaos in a string. Additional non-linear and chaotic behavior is also observed (hysteresis, chaotic transients, period doubling, etc.,...), but we will focus on torus doubling as it is easily observable and persists for a wide range of operating parameters.