Structural response loads in force-limited vibration testing

Flight equipment is exposed to random vibration excitations during launch and is functionally designed to survive a shaker random vibration test. In the test, the random vibration design levels will be applied at the equipment-mounting interface and will be force limited to reduce over-testing at shaker hardmount resonance frequencies. As is commonly practiced for heavier equipment, the equipment also is designed to the structural flight limit load. The philosophy of the Limit Load Factors (LLFs) or so-called the Mass Acceleration Curve (MAC) has been adopted over many years for use in the preliminary structural design of spacecraft and flight equipment. The purpose of the work presented herein is to discuss the results of force limit notching during vibration testing with respect to the traditional limit load design criteria. By using a single-degree-of-freedom (SDOF) system approach, this work shows that with an appropriate force specification the notched response due to force limiting will result in loads comparable with the structural design limit criteria. A simplified formula is presented to predict the test load limits, based only upon estimates for the first significant resonance of the equipment and the semi-empirical force specification factor, C2.