Calculating cross-orthogonality with expanded test data

Abstract

Compatibility In general, math model dynamic degrees-of-freedom (DOF) will not be uniquely one-for-one with accelerometers placed upon the prototypes. Consequently, reduction of the math model will be required. If all accelerometers do not lie directly at math model DOF, this reduction will require more than one step. Following the standard force-free reduction, a second calculation must kinematically transform to juxtaposition. Once developed, of course, the double transformation may be combined into one. This total transformation, applied to the math model mass matrix in a Guyan reduction, satisfies compatibility requirements. The purpose of this Note is primarily to point out that more detailed information is retained if the mass matrix reduced in the above manner is not employed. Rather, the transformation (applied to the test modes) essentially provides for their expansion to math model size. Then the c/o computations will employ as independent quantities all DOF in the analytical modal vectors.