Assessment of the Bill Emerson Memorial Bridge - FTP Directory ...

when data points are sampled at a fixed interval. The inverse form of the DFT is given bythe equation:1 N −12 ikn / Nfn= ∑ F ke π (n = 0,1...N −1) (3.2)N k =0Eqs. (3.1) and (3.2) can be applied to the bridge data analysis. However, these equationsmust be further simplified for practical applications since they require N 2 complexmathematical operations which can take quite a bit computation time even with moderncomputing power. As such, another numerical operation called Fast Fourier Transform(FFT) is used in this study. It can exploit the periodic and symmetric nature oftrigonometric functions to greatly improve the computational efficiency of DFT. Indeed,the number of computations is reduced to N log 2(N) in FFT, which is approximately 100times less than that of the DFT for a set of 1000 data points (Hu and Harik et al., 2006).As pointed out previously, peak picking method is an effective technique in frequencydomain. It has been widely used in practice due mainly to its simplicity and processingspeed. Its associated algorithm, however, involves the averaging of temporal informationand thus loses most of their details. In addition, peak picking method has the followingtheoretical drawbacks:♦ Picking the peaks is always a subjective task:♦ Operational deflection shapes are obtained instead of mode shapes;♦ Only real modes or proportionally damped structures can be deduced by themethod; damping estimates are unreliable.In spite of the above drawbacks, peak picking method is still most popular in civilengineering practice for ambient vibration characteristics.The mode shapes of a tested structure are determined by the relative values of frequencytransfer functions at various natural frequencies. Note that in the context of ambientvibration tests, transfer function does not mean the ratio of response over force, but ratherthe ratio of response measured by a roving accelerometer over the response measured bya reference accelerometer. Therefore, every transfer function yields a mode shapecomponent relative to the reference accelerometer. Here it is assumed that the dynamicresponse at resonance is only determined by one mode. The validity of this assumptionimproves as vibration modes are better separated and as structural damping is lower.The data processing and the modal identification are carried out by implementing thepeak picking method in Matlab version 7.1 developed by MathWorks, Inc. The measureddata in time domain were analyzed in the software and then converted to the frequencydomain by FFT.3.5. Measured data analysisAccording to Figures 3.2 to 3.9, the responses induced by traffic loading are muchweaker than those by the May 1 2005 earthquake. Therefore only the latter is furtheranalyzed in this section to identify the natural frequencies and the approximate modeshapes of the bridge. The Fourier spectra of the measured accelerations at the bridge deck28