On the Application of Response Limiting to Finite Element Structural Analysis Programs

The inclusion of response limiting or “notching” in random vibration design and test requirements for larger equipments such as spacecraft is becoming more commmon. This type of requirement states that the specified input excitation, usually motion, may be reduced in narrow frequency bands to the degree necessary to limit the response at any of a number of specified locations to a specified maximum response. Laboratory test procedures to implement such requirements have been developed and described in the literature. Clearly it is also desirable to include such notching during the design analysis stage when using finite element structural analysis programs typified by NASTRAN. Exact computation of the notched input excitation and associated system responses is quite complicated and therefore costly. This paper describes a simple, economical method of computing the notched spectrum using an approximation which relies only on reasonably separated peak responses at any response control node and a not unusually small difference in level between the maximum input and maximum response spectral density levels. The method accounts for the modal damping, the specified averaging bandwidth for response control, and any desired number of response control nodes, i.e., locations. An interesting by-product of the analysis was the determination that only 50 percent of the mean square response of a single d.o.f. system to white noise is due to the excitation within the resonant or 3 db bandwidth of the system. Some of the implications of this result with respect to spectral analysis procedures and popular methods of estimating the response of systems to shaped random vibration spectra are discussed.