Determination of Notched Input for Equipment Under Random Vibrations

Equipment that is mounted on a spacecraft is subjected to random vibration tests to verify whether they can withstand the specified random loads. These tests are generally carried out by using shaker systems during which equipment experiences very high responses at the natural frequencies of the equipment. To reduce such over-testing, notching of the input is done. Notching of the input is normally carried out by considering the force generated at the base and limiting it to a specified value. To accomplish the notching, the force spectrum to be limited and measurement of base force during the tests are needed. This work shows that the acceleration input at the interface of equipment gets reduced at its resonance frequency and this feature can be utilized in arriving at the notched input. An expression to determine the depth of notching is derived and the results are compared with those obtained using numerical simulations. The depth of the notch increases with the response of the oscillator and it is sensitive to the stiffness ratios rather than the mass ratios of the oscillator and the mounting panel. This behavior and the expressions derived can be effectively used in arriving at the notched input for an equipment without the need for measuring the base force, especially for random vibration testing, which is demonstrated with an example.