Experiments on Large Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 208

source is often impossible and it is necessary to use a technique similar to modal
techniques. This involves selecting a reference measuring position that will stay
fixed during all the tests, and using this to calculate the cross-spectra of the obtained
signals with regard to the reference signal. From this, we can estimate a coherence
function from the cross-spectra [BEN 00]. This indicator varies from 0 to 1. A high
value, associated with a peak on the power spectral density curves, reveals a mode
specific to the structure, whereas local vibration modes lead to low values. Some
examples of power spectral densities and coherence factors are shown in Figure
6.14.
Resonance can be directly identified from PSD curves using the coherence
function as an additional indicator. It is possible to draw the eigenmodes for the
amplitudes and phases associated with each resonance, as is the case with the forced
vibration tests. Damping is often difficult to estimate because of the amount of noise
in PSD curves, as the stress level of the structure under ambient vibrations is
generally very low. To overcome this, a new method for identifying dynamic
properties in the time domain has been developed, and it has been shown to provide
an improved assessment of damping and the vibration modes from ambient vibration
signals [AND 99].
6.4. Application to buildings
The finite element method is used to model very complex large civil-engineering
structures all over the world. The ability of any mathematical model to represent the
real behaviors of the structure can only be validated by comparing analytical results
with experiment results. Obviously, such an approach cannot be achieved at the
project definition stage or during designing, but it does make it possible to verify
designing hypotheses. This method was used during the rebuilding of Montreal's
Olympic Stadium roof, as the dynamic characteristics of the Stadium's tower had to
be determined to extremely high precision. Besides determining the dynamic
characteristics, repeated vibration tests can also be used as an instrument to measure
damage in a structure. This technique has been successfully applied to a two-storey
building subjected to higher and higher seismic stress levels causing appreciable
damage in the structure.