Author
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LU, ZHIQU - UNIV. OF MISSISSIPPI |
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Submitted to: Acta Acustica
Publication Type: Peer Reviewed Journal Publication Acceptance Date: 1/31/2007 Publication Date: 5/31/2007 Citation: Lu, Z. 2007. The phase shift method for studying nonlinear acoustics in a soil. Acta Acustica. 93:542-553. Interpretive Summary: The work presented in the paper shows significant different nonlinear responses between elastic and porous materials. For an elastic material, the resonant frequency and the quality factor are independent of the source amplitude. For porous materials, like the soil in the study, strong nonlinear behaviors are present, manifesting in many ways: resonant frequency shift, rich harmonics (up to the fifth harmonic can be detected), extremely high hysteretic nonlinearity parameters, energy transference, acoustic saturation at the fifth harmonic, and phase shift. The observed relationships between the frequency shift/strain and the phase shift/strain are linear rather than quadratic, supporting the non-classical nonlinear theory. The phase shift method features many advantages over existing methods for studying nonlinear acoustics of materials. (1) The method is based on a phase-lock-in technique, which is inherently immune to noise. (2) The phase comparison method uses a mixer as a phase detector, in which the detected phase output is proportional to the phase difference and the amplitudes of the two compared signals. It is possible to extend the technique to monitor tiny changes in material properties caused by the variation of temperature, pressure, and moisture effects, slow dynamics, and chemical phase transition. In fact, a long-term survey of field soil is underway by using the current phase shift method to study the influence of weather and season on soil properties. The results will be reported elsewhere. (3) The PSD technique compares only the fundamentals from the reference and receiver. The high harmonics in the source and the soil don’t affect the measurement. (4) The method requires very small perturbations. The strain range from 10-7 to 10-6 used in the study is sufficient to create measurable phase shifts without permanently changing the structure of the sample. (5) In contrast to the phase comparison and phase modulation methods, which require either an external pressure source or a second pumping wave, this approach needs only one source for self-phase-modulation. (6) In this study, frequency sweeping has been conducted. However, it is not necessarily required because the phase shift method does not depend on the phase resonant peaks. A fixed frequency may be used for measuring phase shift at an elevating driving amplitude and the test can be conducted at a frequency away from resonance. (7) The frequency response in this study is normalized to the reference, rather than to the applied electrical signal, as performed in most resonant bar tests. The current method provides more accurate measurement on the intrinsic properties of the sample. (8) The capability of harmonic measurement of the lock-in amplifier allows quantitative analysis of the harmonic spectrum, which gives more complete information of material nonlinearity. The study shows many nonlinear acoustic behaviors of a soil, including resonant frequency shift, high harmonic generation, energy transference, and phase shift. It is demonstrated that phase shift, as a counterpart of the resonant frequency shift, can be used for determining the hysteretic nonlinearity parameter of the soil. The results of the phase shift method are in good agreement with that of the resonant frequency shift method. This technique has many advantages over the existing methods for determining the nonlinearity parameter. In addition to the academic interests in studying non-classical nonlinear acoustics, the present method may find its practical applications in the sciences of agriculture, medical diagnosis, landmine detection, geophysical field-test, material characterization, and nonlinear non-destructive evaluation, etc. Technical Abstract: In this paper, a phase shift method for studying nonlinear acoustic behaviors of a soil is described. The method uses a phase-lock-in technique to measure the phase shift caused by increments in the amplitude of an excitation. The measured phase shift as a function of dynamic strain amplitude is used to curve fit the equation of state to extract the hysteretic nonlinearity parameter. It is found that the nonlinearity parameter obtained from this method is in good agreement with that obtained from the frequency shift method. This study also shows many nonlinear acoustic behaviors of the soil including resonant frequency shift, high harmonic generation, energy transference, and phase shift. |
