Page 49 - Shock and Vibration Overview

Response Spectrums

Figure 31: A seven spring system is shown with natural frequencies increasing by a power of 2
between each other.

Figure 32 shows six frames of the response out of these springs as they experience the
shock input. The full video is available to download on Tom Irvine’s vibrationdata page.
One can see the spring on the far left experience very little overall motion but it had to
withstand a significant amount of relative motion and spring compression. On the far

right the spring tracks the base input with very little spring compression. The middle
systems experience widely oscillating acceleration throughout the input and then after
the shock impulse has ended.

Figure 32: From top left to bottom right the frames are spaced approximately 0.25 seconds apart
as the base input goes through a 1 second half sine pulse.

Using the MATLAB GUI package on Tom Irvine’s vibrationdata blog we can calculate the
response out of these systems shown in Figure 33. Notice how the stiffest spring tracks
the input nicely and then quickly rings out after the base excitation is done. The softer
springs also oscillate after the base input is finished but they do so much more slowly

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