Practical improvements to real and imaginary spectral based modal parameter measurements of SDOF systems

For a single degree of freedom system, especially with non-light damping, the use of the real spectral part of either the displacement or velocity responses (or the transfer functions based on them) has the advantages of determining the natural frequency (fn) directly, independent of the response parameter, and providing an accurate measurement for damping (ζ). However, this method is sensitive to spectral phase errors due to temporal misalignment of the signal or due to net inter-channel delay differences caused by signal filtering. Two techniques are presented to correct for these errors; one based on the correct temporal alignment of the impulsive part, and the other on the infimum of the imaginary spectral part. These are first demonstrated using a numerical model, and are shown to facilitate the correct measurement of fn and bring ζ within the expected error limits due to quantisation. Secondly, they are applied to an experimental system and are seen to greatly improve the consistency between measurements using different methods.