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This theory may be applied to the high-speed trains when the speed exceeds the minimum phase velocity of the elastic waves that they induce in the track.
It is shown that when the velocity of the bogie exceeds the minimum phase velocity of waves in the beam, the vibration of the system may become unstable.
The paper analyzes the case when the complex bogie system exceeds the minimum phase velocity of waves in the beam, which may lead to the vibration of the system becoming unstable.
The measured dynamic response is analyzed in detail, and it is shown that the critical speed is controlled by the minimum phase velocity of the first Rayleigh mode of the soil and embankment profile at the site.
It is assumed that the masses and the beam are in continuous contact and that the velocity of the oscillators exceeds the minimum phase velocity of waves in the supported beam.
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Since we search the maximum peaks within the wavenumber windows that we set a priori, the minimum phase velocities are limited, but the maximum ones are not.
Moreover, we also searched maximum (Cmax) and minimum (Cmin) phase velocities for each frequency and exclude unreliable phase velocities with a significance level of 5% of (Cmax − Cmin).
If we are using a maximum frequency of 8 Hz, and assuming a phase velocity of 700 m/s, the minimum expected wavelength is about 90 m.
The MCS data were first processed following a conventional procedure that includes minimum phase conversion, predictive deconvolution, common midpoint (CMP) sorting, velocity analysis, normal moveout, stacking, and post-stack time migration (PoSTM).
The frequency spectra of the surface displacements show that resonant peaks occur at frequencies where the group velocity vanishes and the phase velocity remains finite, i.e., a minimum in the dispersion curve below the cut-off frequency.
When no minimum fitting was found within the search range, we stopped measuring the phase velocity in the following bands.
More suggestions(15)
minimum fluidisation velocity
minimum phase channel
minimum phase difference
minimum phase residue
minimum phase assumption
minimum fluidization velocity
minimum surface velocity
minimum phase single-degree-of-freedom
minimum meltpool velocity
minimum phase argument
minimum phase lag
minimum air velocity
minimum phase model
minimum phase nonlinear
minimum phase state
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