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Self-modulation and recurrence phenomena in vibrator-induced, steady-state sinusoidal ground vibration

1988; Elsevier BV; Volume: 50; Issue: 1 Linguagem: Inglês

10.1016/0031-9201(88)90095-7

1872-7395

P. P. Dimitriu,

Seismic Waves and Analysis

Results of an experimental investigation of the evolution of vibrator-induced, steady-state sinusoidal ground vibration are reported and interpreted as suggesting the nonlinear wave phenomenon known as Fermi-Pasta-Ulam recurrence. Uniform-amplitude (unmodulated) sinusoidal wavetrains were generated by a 4441 N electrodynamic vibrator, the vertical force being used, and the evolution of the wavetrains was monitored on the ground surface by eight vertical seismometers. Two locations, 6 m apart, were used to install the vibrator. The seismometers were aligned along three profiles: two for the first location of the vibrator (30 and 60 m long) and one for the second (73 m long). The wavetrain carrier frequency was varied from 7 to 14.65 Hz; its amplitude measured from 0.015 to 0.6 cm s−1 at 1 m from the source. Whenever a wavetrain was generated with a Mach number below some critical value (∼ 10−5 at 1 m from the vibrator), it evolved in a recurrent manner. The Fourier spectra of the records show that, during the initial stage of evolution, an instability developed resulting in a dramatic growth of the second and third harmonics, whose appearance is attributed to ground nonlinearity (harmonic generation), and their lower sideband components. As the instability effects reached their peak levels, the wavetrain seemed to be losing its coherence, often becoming strongly modulated (self-modulation). With increasing propagation distance, however, the energy gradually returned to the carrier component, and the wavetrain demodulated, recovering its original (uniform and coherent) form (recurrence). Despite some important peculiarities, the unstable wavetrain evolution observed is believed to belong to the class of nonlinear wave phenomena known as Fermi-Pasta-Ulam recurrence. Since, by theory, recurrence involves solitons, the results also imply the existence of seismic solitons.