Abstract

DETC99/VIB-8130

TIME-VARYING CROSS-SPECTRA BY HARMONIC WAVELETS FOR SOIL MOTION WITH DAMAGE

In order to simulate the behavior of large soil structures in the laboratory, scale models are subjected to an artificially high gravity field in a centrifuge. To simulate the dynamic strain conditions produced in the soil by the motion of an earthquake, the model is subjected to short-term transient shear deformation. This is achieved by applying a sudden burst of lateral oscillatory movement by a mechanical actuator. Measurements of the soil model’s acceleration response are recorded by an array of accelerometers during the model’s transient shaking phase. This paper is about analyzing the transient vibration data that is obtained. Calculations are carried out by the harmonic wavelet method and time-frequency maps generated to show (1) wavelet amplitude for each accelerometer signal, (2) the product of wavelet amplitudes for two accelerometer signals, and (3) the relative amplitude between two signals. It is shown that, in the limiting case when the harmonic wavelets have infinite bandwidth (i.e. they become pure harmonics), the results obtained are identical with the amplitude of the power spectral density and the amplitude and phase of the cross spectral density for the signals involved. In the general case, this approach is used to define the time-varying power and cross spectral densities for transient signals.

A typical time-frequency map is reproduced above. It shows the phase of the time-varying cross spectral density between two signals. One of these two signals is shown as the input in the top figure and lasts for 2 seconds, with the shaking phase filling about half the time window. The amplitude of its power spectral density is plotted on edge at the left side with a frequency scale running from zero to 180 Hz.

This time-frequency map for phase shows how the phases of the two signals change with time and frequency. The density scale at the right side of the map shows the angle range covered which is from π (top) to – π (bottom) of the scale. The significance of the diagram and the conclusions that may be drawn from it are discussed in the paper.

Keywords: wavelet, cross-spectrum, harmonic, transient, centrifuge

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1999 by ASME