Root Mean Square Spectrum Research Articles

Sensitivity of road unevenness indicators to short wavelength distresses in Portland cement concrete surfaces

This paper examined the sensitivity of 20 road unevenness indicators (RUIs) for local discontinuities (various distresses, joints, joint and surface defects, cracks, spalls, other road features, humps, dips, etc.) of a maximum length of 20 cm in Portland cement concrete pavements. Approximately, 5500 road records totalling 530 km from the Long-Term Pavement Performance programme were processed. Raw profiles were separated into random and distress components using a median filtering method. The median filter was set to identify distress of a maximum length of 20 cm and with a minimal height of 3 mm. Over 26,000 distresses and their dimensions were identified. Raw longitudinal road profiles were compared with the separated pure random components. The most sensitive indicators of distresses were road elevation spectrum parameters in whole- and short-wave bands, the Profile Index and the road elevation root mean square (RMS) value in the short-wave band. Negligible sensitivity was observed for the International Roughness Index, road elevation RMS values and spectrum parameters in long- and medium-wave bands. The influence of road data pre-processing on the results was estimated.

Origin of the characteristic X-ray spectral variations of IRAS 13224−3809

Abstract The narrow-line Seyfert 1 galaxy (NLS1) IRAS 13224−3809 is known to exhibit significant X-ray spectral variation, a sharp spectral drop at ∼7 keV, strong soft excess emission, and a hint of an iron L-edge feature, which is very similar to the NLS1 1H 0707−495. We have proposed the “Variable Double Partial Covering (VDPC) model” to explain the energy spectra and spectral variability of 1H 0707−495 (Mizumoto et al. 2014, PASJ, 66, 122). In this model, the observed flux/spectral variations below 10 keV within ∼ a day are primarily caused by change of the partial covering fraction of patchy clouds composed by double absorption layers in the line of sight. In this paper, we apply the VDPC model to IRAS 13224−3809. Consequently, we have found that the VDPC model can explain the observed spectral variations of IRAS 13224−3809 in the 0.5–10 keV band. In particular, we can explain the observed root mean square (RMS) spectra (energy dependence of the fractional flux variation) in the entire 0.5–10 keV band. In addition to the well-known significant drop in the iron K-band, we have found intriguing iron L-peaks in the RMS spectra when the iron L-edge is particularly deep. This feature, which is also found in 1H 0707−495, is naturally explained with the VDPC model, such that the RMS variations increase at the energies where optical depths of the partial absorbers are large. The absorbers have a larger optical depth at the iron L-edge than in the adjacent energy bands, and thus a characteristic iron L-peak appears. On the other hand, just below the iron K-edge, the optical depth is the lowest and the RMS spectrum has a broad dip.

Universal response spectrum procedure for predicting walking-induced floor vibration

Floor vibrations caused by people walking are an important serviceability problem both for human occupants and vibration-sensitive equipment. Present design methodologies available for prediction of vibration response due to footfall loading are complex and suffer from division between low and high frequency floors. In order to simplify the design process and to avoid the problem of floor classification, this paper presents a methodology for predicting vibration response metrics due to pedestrian footfalls for any floor type having natural frequency in the range 1–20Hz.Using a response spectrum approach, a database of 852 weight-normalised vertical ground reaction force (GRF) time histories recorded for more than 60 individuals walking on an instrumented treadmill was used to calculate response metrics. Chosen metrics were peak values of 1s peak root-mean-square (RMS) acceleration and peak envelope one-third octave velocities. These were evaluated by weight-normalising the GRFs and applying to unit-mass single degree of freedom oscillators having natural frequencies in the range 1–20Hz and damping ratios in the range 0.5–5%. Moreover, to account for effect of mode shape and duration of crossing (i.e. duration of dynamic loading), the recorded GRFs were applied for three most typical mode shapes and floor spans from 5m to 40m.The resulting peak values as functions of frequency i.e. spectra are condensed to statistical representations for chosen probability of being exceeded over a wide range of applications. RMS (acceleration) spectra show strong peaks corresponding to the first harmonic of pacing rate followed by clear minima at approximately 3.5Hz, a second much smaller peak corresponding to the second harmonic and a steady decline with increasing frequency beginning around 5Hz. One-third octave spectra show asymptotic trends with frequency, span and damping.A comprehensive validation exercise focusing on the acceleration RMS spectra was based on a representative range of floor samples for which modal properties had been identified and walking response studied during experimental campaigns of vibration serviceability evaluation. Due to the statistical approach an exact validation would not be possible, hence measured peak RMS values were matched to distributions for the equivalent idealised structure. In the vast majority of cases the measured values, intended to represent worst-case conditions, fitted the upper decile of the corresponding simulated spectra indicating consistency with the proposed approach.