Cogwheel load: a new forced vibration test for bridges?

Abstract

A moving impulse load generated by a rolling heavy polygonal wheel with a constant velocity, called here the cogwheel (CW), could be used as a testing excitation for bridges. This type of dynamic load, already proposed in an earlier article, acts along the entire driving path, its intensity is adjustable, and it can be very efficient in the case of resonance. It is a combination of static and dynamic loading tests, which requires only one or a few transducers mounted on the bridge, and traffic interruption of only a few minutes. The dynamic response contains higher harmonic components, and the moving mass alters the dynamic properties continuously during the passage, which should be considered while assessing the condition of the tested structure. The high capability of indication of frequency changes is explained and demonstrated in a new scaled laboratory test. Suggestions for damage localisation are also made. It is foreseen for testing of short- and medium-sized bridges on the occasion of commissioning and periodical checks after further research.

Appendix: Other tested tools for the evaluation of spectral changes

Following concepts are aimed at numerical evaluation of spectral changes.

The amplitudes (spectral lines) can either increase or decrease in the case of a damage, depending on the relative position of the traced frequency line towards the natural frequencies (before or after, respectively). The following expression can be used to estimate the amplitude changes in a chosen frequency band around a natural frequency:

$$di=\frac{{\sum }_{j=lf}^{uf}{PSD}_{j,d} -{PSD}_{j,0}}{{\sum }_{j=lf}^{uf}{PSD}_{j,0}}\left[\mathrm{\%}\right],$$

(3)

where lf and uf represent the lower or upper limit of the frequency band of interest, respectively. Zero indicates the intact (reference) condition and d the damaged condition. Equation (3) can also be used for discrete frequency lines (lf = uf). An a priori knowledge of the position of the natural frequencies is the necessary condition for application of the Eq. (3) and the evaluation of the increase or decrease is left to an engineering judgement.

The frequencies of the spectrum shift to lower frequencies in the case of a damage. Shifts of the magnitude of at least the resolution of the spectra can be detected in the measured PSD at the location of natural frequencies. A smaller change can be detected as a change of PSD momentum in a moving window w according to Eq. (4):

$$df=\sum_{{\acute{i} }=lf}^{uf}\left(\frac{{\sum }_{j=x-w/2}^{i+w/2}{F}_{j,d}\bullet {PSD}_{j,d}}{{\sum }_{j=i-w/2}^{i+w/2}{PSD}_{j,d}}-\frac{{\sum }_{j=i-w/2}^{i+w/2}{F}_{j,0}\bullet {PSD}_{j,0}}{{\sum }_{j=i-w/2}^{i+w/2}{PSD}_{j,0}}\right)[\mathrm{Hz}].$$

(4)

F_j indicates a frequency here. However, data under the noise level can cause a considerable bias of the estimation according to Eq. (4).

1.1 Experimental results

Application of Eq. (3) supplied reliable estimations beginning with the damage case + 150 g, because at the frequency of 27.7 Hz would not estimate the damage correctly (see Fig. 8) for the case + 100 g, for example.

Application of Eq. (4) worked well from the damage case + 100 g. It seems to be suitable for automatic applications.