Spectral Density Matrix Transformations

Abstract Reference criteria for a multiple degree-of-freedom (MDOF) random vibration test is generally provided in terms of an acceleration-based spectral density matrix (SDM). This SDM may be developed in terms of the auto-spectral densities (ASDs) and cross-spectral densities (CSDs) computed from the time histories acquired from an appropriately placed and oriented set of linear accelerometers. Such a direct measurement linear accelerometer based reference criteria will be denoted as SDMmeas. A second technique for defining a reference SDM is in terms of the accelerations associated with the six classical motion degrees-of-freedom as defined at an arbitrary point of origin. Such a reference will be denoted as SDMmotion. The objective at hand is to demonstrate the method of transforming between these two reference criteria spaces.