Force-limited vibration complex two-degree-of-freedom system method

Force-limited vibration testing developed at the Jet Propulsion Laboratory offers many opportunities to decrease the overtesting problem associated with traditional vibration testing. Among the force-limited vibration methods, the complex two-degree-of-freedom system (TDOFS) appears to be the most complete and versatile model that gives reasonably conservative force limits and does not require extrapolation of interface force data for similar mounting structures and test articles. However, there are some limitations to the complex TDOFS model. The model is well adapted for nicely separated modes, but issues regarding the closely space modes have not been fully addressed in the literature. Also, the complex TDOFS model is based on free boundary conditions for the mounting structure, which appear to be natural for many cases such as spacecraft mounted on a launch vehicle. However, this is not necessarily true for some other cases such as an electronic component mounted on a spacecraft antenna, which requires fixed boundary conditions. Greater insights into the complex TDOFS method are given, and methodologies to overcome its limitations are proposed. It is shown that a simple approach can be used to assure conservative estimate of the force limits in situations regarding closely spaced modes. It is also demonstrated that, although the complex TDOFS method is not perfectly adapted to fixed boundary conditions of the mounting structure, given certain precautions, it still provides good estimates of the force limits.