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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.
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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.
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 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.
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.
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).
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 phase velocities are then inverted for fundamental-mode Rayleigh phase velocity maps at a grid spacing of 0.3°, at periods from 10 to 100 s.
One-dimensional models of shear wave velocity for the eastern Mediterranean obtained from the inversion of Rayleigh wave phase velocities and tectonic implications.
Profiles of attenuation coefficients and phase velocities.
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CEO of Professional Science Editing for Scientists @ prosciediting.com