Dynamics: Resonance

Measurement of the resonance frequency of a building

Fig.16-17: Frequency spectrum in one main direction of the building shown in Fig. 15-17 [16.10]

The concept of resonance can be used to identify the natural frequencies of a structure. A harmonic force with appropriate amplitude is applied to the structure and the corresponding maximum structural response is then recorded. The procedure is repeated a number of times with different forcing frequencies. The frequency corresponding to the largest value of these maximum responses is the resonant frequency of the structure. As civil engineering structures have damping ratios far less than 10%, the resonance frequency measured from the forced vibration is actually the natural frequency of the structure, as shown in Table 16-2.

Among a number of experiments carried out on the test building shown in Fig. 15-17 were forced vibration tests with vibration generators used to shake the structure in a controlled manner at frequencies within the range 0.3 Hz to 20 Hz [16.10]. Four vibration generators were placed at the four corners of the roof of the building and the building response was monitored using accelerometers aligned to the measure motions in appropriate directions. The response of the building was sampled using optimised filtering, amplification and curve fitting and then normalised by converting the measured accelerations to equivalent displacements which were then divided by the applied forces. The maximum normalised displacement corresponding to a particular load frequency was plotted as a cross in Fig. 16-17. This process was repeated for a number of load frequencies to produce many crosses in Fig. 16-17, which are linked by a best-fit one degree-of-freedom curve. The frequency corresponding to the largest response is a resonance frequency of the structure. For this building the resonant frequency was 0.617 Hz in one main direction. This technique has been widely used in structural engineering, mechanical engineering and other areas.