The Cross Spectrum in Multiple Input Multiple Response Vibration Testing

Abstract

Random vibration tests have been conducted for over 5 decades using vibration machines which excite a test item in uniaxial motion. With the advent of multi shaker test systems, excitation in multiple axes and/or at multiple locations is feasible. For random vibration testing, both the auto spectrum of the individual controls and the cross spectrum, which defines the relationship between the controls, define the test environment. This is a striking contrast to uniaxial testing where only the control auto spectrum is defined.

In a vibration test the energy flow proceeds from drive excitation voltages to control acceleration auto and cross spectral densities and finally, to response auto and cross spectral densities. This paper examines these relationships, which are encoded in the frequency response function. Following the presentation of a complete system diagram, examination of the relationships between the excitation and control spectral density matrices is clarified. It is generally assumed that the control auto spectra are known from field measurements, but the control cross spectra may be unknown or uncertain. Given these constraints, control algorithms often prioritize replication of the field auto spectrum. The system dynamics determine the cross spectrum. The Nearly Independent Drive Algorithm, described herein, is one approach.

A further issue in Multi Input Multi Response testing is the link between cross spectrum at one set of locations and auto spectra at a second set of locations. The effect of excitation cross spectra on control auto spectra is one important case, encountered in every test. The effect of control cross spectra on response auto spectra is important since we may desire to adjust control cross spectra to achieve some desired response auto spectra. The relationships between cross spectra at one set of locations and auto spectra at another set of locations is examined with the goal of elucidating the advantages and limitations of using control cross spectra to define response auto spectra.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525