Question

Describe the procedure to determine the first modal damping. Outline the key steps and sketch the collected acceleration data.

Answer 1

Damping properties are of significant importance in determining the dynamic response of structures, and accurate prediction of them at the design stage, especially in the case of light-weight, wind-sensitive buildings, is very desirable. Unfortunately, damping parameters can not be deduced deterministically from other structural properties and recourse is generally made to data from experiments conducted on completed structures of similar characteristics. Such data is scarce but valuable, both for direct use in design and for furthering research into the phenomenon and modelling of damping.

Key steps to follow:

Preliminary tests together with theoretical modelling pointed to four measurable natural frequencies, two predominantly translational and two predominantly torsional (due to small asymmetries in the structure the modes were not purely translational or torsional). The three main types of test carried out were as follows:

Free vibration decay :The structure was vibrated at a resonant frequency until it settled into a steady state at which point the mechanical exciter was brought to a sudden stop leaving the structure to vibrate freely until brought to rest by the effects of damping. The resulting damped free vibration record could then be used with methods such as the well-known log-decrement to determine the equivalent viscous damping coefficient. Whilst this approach is ideal for the lowest mode, it becomes progressively more difficult with the higher modes due to their tendency to revert to the lowest mode as decay proceeds and it was successfully applied to only the two lowest modes (one translational and one torsional). Tests were conducted with three different amplitudes of excitation (corresponding to the 10, 20 and 40kg eccentric mass sets).

Frequency sweep : Frequency sweep testing was used to determine acceleration and displacement response spectra by operating the exciter at a range of gradually incrementing frequencies and recording the steady state response data at each increment. Peaks in the resulting spectra indicated natural frequencies, so in order to generate data from which damping results could be deduced with maximum accuracy, the frequency sweep was repeated in the vicinity of the peaks with smaller increments (approx. 0.005Hz). Because eccentric mass type exciters generate forces which are proportional to the square of the excitation frequency, ? , the recorded data was generally normalised by dividing by 2 ? . .

Mode shapes : Mode shape tests were conducted by distributing accelerometers at different levels down the building, exciting the structure at each resonant frequency, and recording accelerations at the same instant. Double integrating of the acceleration records permitted displacement records to be obtained, revealing the mode shapes. Pairs of parallel oriented accelerometers, spaced apart, enabled separation of torsional and translational displacements.