Development of a force specification for a force-limited random vibration test

Vibration testing, techniques have been developed and employed that reduce the overtesting caused by the essentially infinite mechanical impedance of the shaker in conventional vibration tests. With these ``force-limiting`` techniques, two vibration test specifications are used: the conventional acceleration specification, and an interface force specification. The vibration level of the shake table is controlled such that neither the table acceleration nor the force transmitted to the test item exceeds its specification, hence the name ``dual control`` vibration test. The effect of limiting the shake table vibration to the force specification is to reduce (``notch``) the shaker acceleration near some of the test item`s resonance frequencies. Several methods of deriving the force specification have been described in the literature. A new method is proposed in this paper that is based on a modal method of coupling two dynamic systems, in this case the ``source`` or launch vehicle, and the ``load`` or payload. The only information that is required is an experimentally-measurable frequency-response function (FRF) called the dynamic mass for both the source and the load. The method, referred to as the coupled system, modal approach (CSMA) method, is summarized and compared to an existing method of determining the force specification for force-limited vibration testing