Identification of damping: Part 4, error analysis

In previous papers (S. Adhikari and J. Woodhouse 2001 Journal of Sound and Vibration 243, 43-61; 63-88; S. Adhikari and J. Woodhouse 2002 Journal of Sound and Vibration 251, 477-490) methods were proposed to obtain the coefficient matrix for a viscous damping model or a non-viscous damping model with an exponential relaxation function, from measured complex natural frequencies and modes. In all these works, it has been assumed that exact complex natural frequencies and complex modes are known. In reality, this will not be the case. The purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors. By using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting. Indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour.

Investigation of damping effects on statistical energy analysis of coupled structures

The effects of damping on energy sharing in coupled systems are investigated. The approach taken is to compute the forced response patterns of various idealised systems, and from these to calculate the parameters of Statistical Energy Analysis model for the systems using the matrix inversion approach [1]. It is shown that when SEA models are fitted by this procedure, the values of the coupling loss factors are significantly dependent on damping except when it is sufficiently high. For very lightly damped coupled systems, varying the damping causes the values of the coupling loss factor to vary in direct proportion to the internal loss factor. In the limit of zero damping, the coupling loss factors tend to zero. This is a view which contrasts strongly with 'classical' SEA, in which coupling loss factors are determined by the nature of the coupling between subsystems, independent of subsystem damping. One implication of the strong damping dependency is that equipartition of modal energy under low damping does not in general occur. This is contrary to the classical SEA prediction that equipartition of modal energy always occurs if the damping can be reduced to a sufficiently small value. It is demonstrated that the use of this classical assumption can lead to gross overestimates of subsystem energy ratios, especially in multi-subsystem structures. © 1996 Academic Press Limited.