Keywords: dynamic displacement measurement, kinematical acceleration, moving load, structural eigenfrequency.

Large structures do not always have easy access to points that need monitoring; in those circumstances it is practical to use laser based measuring instrumentation, which typically measures displacements. In case of dynamic measurements under moving load when we are recording displacements instead of accelerations or velocities dominant values belong to static displacements. This paper demonstrates some techniques for avoiding the dificulties in the interpretation of the results from dynamic displacement measurements.

Lately new equipment for measuring displacement instead of acceleration is appearing with fairly large numbers of them being based on laser devices. The main reason for introducing such devices is their ability to acquire data without direct contact with the structure under consideration. If the device is capable of dynamic data acquisition then one device could be used for static as well as dynamic measurements. Eigenfrequencies are extracted using discrete Fourier transformation (DFT) as in acceleration-based measurements. The question is whether there is any difference in results obtained performing DFT on dynamic displacements or on accelerations. In all the problems and examples considered it is assumed that the accuracy of the results presents no problems.

Structures with fixed position of dynamic forces are characterized with artificial loading such as some kind of oscillating machinery have the homogeneous solution of the system of differential equations in the form and then the acceleration is . Both equations contain the same information but the accelerations are scaled with squared frequency so higher frequencies would have higher amplitudes in the power spectra. The consequence is that measurement of the dynamic displacements is better suited to large civil engineering structures where lower frequencies are of greater significance.

For a moving force it is not necessary to change in time in order to produce dynamic effects in a structure. Actually we could separate the dynamic behavior into two parts: one belonging to oscillations of the structure due to structural masses and the other belonging to changes in deflection due to the speed of the moving force. The fact that the moving force produces both static and dynamic displacements has to be taken into account when considering data obtained from dynamic displacement measurements on structures with the moving load. The displacementa are separated by decomposition of the displacement vector into global and local parts where the global part describes the movement of the centerline of a structure and the local one describes displacements around it. In this way accelerations are separated, too. According to Wilson [2] numerical derivations of dynamic displacements should be avoided as inaccurate. This paper suggests that the static displacements should be separated from the dynamic displacements before proceeding with the frequency analysis.

For testing purposes analytical expressions for displacements and accelerations are derived for a simple beam under the influence of the moving force since that is the case where we could get all the terms in analytical form. Some expressions are taken from Kozar and Štimac [1].

Numerical examples have been performed and the disturbing influence of static displacement is clearly observable. From the numerical examples it follows that in some cases static component can be separated in the frequency domain but in some it can not, in which case it is suggested that static displacements should be numericaly obtained. Results in the frequency domain obtained in this manner are typically superior to accelerations obtained through numerical derivation of the displacements.

For carefully selected loading speeds elastic static components of the displacement can be extracted from the recording of dynamic displacements and used for other purposes.

1

Kozar I, Štimac I, "Numerical Modelling of Beam Wave Equation", in Proceedings of 1st Symposium Computing in Engineering, Zagreb, Hrvatska, 4-6.12.2003., Faculty of Civil Engineering, Zagreb, p. 33 - 40, 2003.

2

Wilson E, "Three-Dimensional Static and Dynamic Analysis of Structures", CSI, Berkeley, California, USA, 2002.

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