Traffic-induced building vibrations in Montréal - National Research ...

740Can. J. Civ. Eng. Vol. 24, 1997Fig. 2. Typical acceleration signals induced by (a) emptybusand(b) loaded truck at 50 km/h.using digital filters of the recursive type, which conform tospecifications of band-limiting and band-pass filters for frequencyweightings W xy and W z per ISO 8041 (ISO 1990b) inthe horizontal and vertical directions, respectively (see Al-Hunaidiand Guan (1996) for details). Root-mean-square values of frequency-weightedacceleration signals were then calculated usingthe same integration time and discarding the same numberof initial averages as for the 1/3 octave band analysis describedabove.Narrow-band frequency analysisNarrow-band frequency analysis using the fast Fourier transform(FFT) was performed in order to resolve in detail thefrequency content of the measured vibration signals. Thenumber of points used in FFT calculations was large enough tocontain the major part of the signal. This eliminated the needfor smoothing windows, hence avoiding difficulties associatedwith these windows in the analysis of transient signals (Al-Hunaidiet al. 1994).Transfer functionsTransfer functions (i.e., ratios) between different measurementpoints were calculated for both the 1/3 octave band and frequency-weightedacceleration values. Transfer functions werefirst calculated for acceleration values obtained for each vehiclepass-by. Then a mean value was calculated from threevehicle pass-bys for the same test.It should be noted that unlike transfer functions obtainedfrom usual spectral analysis methods, the method describedabove does not provide a measure for judging whether the vibrationsignals at the two particular points used in the transferfunction calculation are coherent, i.e., generated by the samesource. In this study, coherence between vibration signals wasverified in two ways. First, a comparison was made betweenambient vibration values and those due to test vehicles. In thefrequency range of 8 to 25 Hz it was found that vibrations inducedby test vehicles are much higher than ambient vibrations;elsewhere this was not so. This was taken as an indication ofcoherent signals only for 1/3 octave frequency bands from 8 to25 Hz. Second, in the frequency range for 1/3 octave frequencybands between 8 and 25 Hz, the minimum and maximum oftransfer functions obtained for each band from three test repetitionswere compared. In most cases, there were insignificantdifferences and again this was taken as an indication of coherencebetween the signals in the said frequency range.© 1997 NRC Canada