. Airborne radar. Airplanes; Guided missiles. 700 MECHANICAL DESIGN AND PACKAGING If the single mass and spring of Fig. 13-7 were to be replaced with a more complex system, the single resonant "mode" of Fig. 13-8 would be replaced by a number of resonant modes equal in number to the degrees of freedom possessed by the system. Each mode of vibration would be characterized by a resonant frequency and a ^. It can be seen that for complex electronic equipment in an environment of sinusoidal vibration, the most damaging structural effects will occur at the resonant frequencies of the vari
. Airborne radar. Airplanes; Guided missiles. 700 MECHANICAL DESIGN AND PACKAGING If the single mass and spring of Fig. 13-7 were to be replaced with a more complex system, the single resonant "mode" of Fig. 13-8 would be replaced by a number of resonant modes equal in number to the degrees of freedom possessed by the system. Each mode of vibration would be characterized by a resonant frequency and a ^. It can be seen that for complex electronic equipment in an environment of sinusoidal vibration, the most damaging structural effects will occur at the resonant frequencies of the various modes. If the excitation of the system ( the motion of the structure) of Fig. 13-7 is random, the response of the mass will necessarily be random; its time history, however, will look quite unlike that of the excitation. For a single degree of freedom resonant system with little damping, the time plot of the response is rather similar to that of the excitation as viewed through a narrow-band filter. A brief sample of the acceleration response of such a system is shown in T? no Mu ^- f c- 1 !-> Fig- 13-9. It can be seen that the l^iG. 13-9 Vibration of Single-Degree- ° of-Freedom Resonant System Excited curve looks much like a sine wave by Random Vibration. with the resonant frequency of the system, but with a continually changing amplitude and phase. If the acceleration density of the structure motion is known in the region of the resonant frequency, the rms acceleration of the mass may be ob- tained. Let aM = rms random acceleration of the mass, g G ^ acceleration density of structure, ^^/cps Q = undamped natural frequency of the system of Fig. 13-7 (or of a normal mode of a more complex system), rad/sec ^ = maximum transmissibility for the corresponding mode. Then um = h^JG^. To sum up, the response of a resonant system to random vibration is a motion very similar to a sine wave at the resonant frequency of the system. The rms acceleration of the response is direc
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