ANÁLISIS DE RESULTADOS

Figure 3.31 shows a short length of I-section beam. The section had been removed from a wrought iron railway bridge in Llangamarsh Wells in South Wales and is typical of many bridges throughout the United Kingdom. The beam is approximately 2.3 m in length and 0.9 m in depth. The length of the beam is insufficient to investigate it’s low frequency ‘bending’ behaviour in the frequency range of interest, however the depth is sufficient for investigating it’s high frequency ‘in-plane’ behaviour. The web has a thickness of 0.01 m. The beam has flanges on each end of the web, making up the I-section. The upper flange is 0.45 m wide with a thickness of 0.03 m. The lower flange is 0.57 m wide and 0.03 m thick. The beam was supported at each end on two wooden blocks. It can also be seen in

Figure 3.31 that the beam’s cross-section is not homogeneous along its length, unlike the finite element models studied in Sections 3.1 and 3.2. There are lumps of wrought iron welded to the bottom flange at one end of the beam and a cross-member connecting the upper and lower flanges near the centre of the beam. Many years of weathering also means that the beam is in an advanced state of deterioration.

In order to validate the model for the driving point mobility of an I-section beam derived in Sections 3.3 to 3.6, mobility measurements were performed on the I-section beam.

Figure 3.31.A short length of wrought iron I-section beam removed from a railway bridge in Llangamarsh Wells in South Wales.

3.7.1. Measurement method

The beam was excited by at a point directly above the beam web using an impact hammer. The response to the impact excitation was measured using an accelerometer located as close as possible to the excitation. The force and response of six to eight hammer taps were recorded to provide some averaging and to reduce the effect of noise in the final result. The driving point accelerance was calculated using an FFT analyser. To obtain a spatial average of the accelerance, the test was performed at five points along the length of the beam and the average of the five results was taken. Finally the accelerance was integrated once to give the driving point mobility Y(f) and converted to one-third octave bands to provide a frequency- averaged result.

3.7.2. Measurement results and discussion.

Figure 3.32 shows the real part of the driving point mobility measured on the bridge beam plotted in one-third octave bands between 600 Hz and 8000 Hz. Results are not plotted below 600 Hz due to signal-to-noise problems. The high mass and high bending stiffness of the beam studied meant that it was difficult to excite the beam with sufficient energy at low

frequency. Results for lower frequencies may have been achieved using an impact hammer with higher mass or a softer tip than the one used in this experiment, but the mobility of the beam at high frequencies is of most interest here.

Also plotted in Figure 3.32 is the predicted real part of the combined mobility of the flange and web plates according to equation (3.11). This result is plotted from approximately 1 kHz (the prediction of the occurrence of the transitional mode according to equation (3.27) for this case) up to 10 kHz. The measured mobility fluctuates around the predicted mobility in this region. The fluctuations were also seen in the finite element results for the flanged beams in Section 3.2.2 and are likely to be due to coupling between the flange-flapping modes and the web compression modes of the beam. The predicted mobility provides a good approximation of the frequency-averaged real part of the driving point mobility in this region.

Using the transitional mode as a marker, the mobility for the transitional range (section 3.4) increasing with the square of frequency up to the transitional mode has also been plotted in Figure 3.32. Although there is little measurement data in this range it can be seen that this result is consistent with the frequency-averaged mobility in this region. Furthermore the prediction of the transitional mode according to equation (3.27) is consistent with the behaviour seen in the measured results.

bridge beam; −−, calculated using equations developed in this section.

3.8. SUMMARY

By comparison with Finite Element results it has been shown that the Timoshenko beam formulation considered in the last chapter is appropriate for low frequencies but at high frequencies local deformation of the beam has to be taken into account. Depending on the depth of the beam these effects can commence as low as 200 Hz (Janssens & Thompson, 1996) although for the 1 m deep beams considered here the lower limit of such effects is about 1 kHz. Models for the various phenomena have been developed to allow physical understanding and these have been implemented in simple formulae.

In modelling bridge noise the coupled beam formulation of Chapter 2 can be used up to and including the decoupling frequency (usually well below 1 kHz) and the improved beam mobilities can be used at higher frequencies.

A summary of the equations needed to model the mobility of an I-section beam throughout the full frequency range is shown in Bewes, Thompson & Jones (2003).