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.
Six degree of freedom (6-DOF) subsystem/component testing is becoming a desirable method, for field test data and the stress environment can be better replicated with this technology. Unfortunately, it is a rare occasion where a field test can be sufficiently instrumented such that the subsystem/component 6-DOF inputs can be directly derived. However, a recent field test of a Sandia National Laboratory system was instrumented sufficiently such that the input could be directly derived for a particular subsystem. This input is compared to methods for deriving 6-DOF test inputs from field data with limited instrumentation. There are four methods in this study used for deriving 6-DOF input with limited instrumentation. In addition to input comparisons, response measurements during the flight are compared to the predicted response of each input derivation method. All these methods with limited instrumentation suffer from the need to inverse the transmissibility function.
Recent advances in 6DOF testing has made 6DOF subsystem/component testing a preferred method because field environments are inherently multidimensional and can be better replicated with this technology. Unfortunately, it is rare that there is sufficient instrumentation in a field test to derive 6DOF inputs. One of the most challenging aspects of the test inputs to derive is the cross spectra. Unfortunately, if cross spectra are poorly defined, it makes executing the tests on a shaker difficult. In this study, tests were carried out using the inputs derived by four different inverse methods, as described in a companion paper. The tests were run with all 6DOF as well with just the three translational degrees of freedom. To evaluate the best way to handle the cross spectra, three different sets of tests were run: with no cross terms defined, with only the coherence defined, and with the coherence and phase defined. All of the different tests were compared using a variety of metrics to assess the efficacy of the specification methods. The drive requirements for the different methods are also compared to evaluate how the specifications affect the shaker performance. A number of the inverse methods show great promise for being able to derive inputs to a 6DOF shaker to replicate the flight environments.