Page 501 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

A

Specifications
of Vibration Bounds

Specifications for vibrations are often based on harmonic motion.
jc = JC() sin cot

The velocity and acceleration are then available from differentiation and the
following relationships for the peak values can be written.

= 2vfx^^
X,) = = - i T T f x ^
These equations can be represented on log-log paper by rewriting them in the
form
In i() = In JTo -h In l i r f
In — In —In l i r f

By letting = constant, the plot of In Xq against In 2tt/ is a straight line of slope

equal to +1. By letting = constant, the plot of In vs. In27r/ is again a
straight line of slope - 1. These lines are shown graphically in Fig. A-1. The graph
is often used to specify bounds for the vibration. Shown in heavy lines are bounds
for a maximum acceleration of 10^, minimum and maximum frequencies of 5 and
500 cps, and an upper limit for the displacement of 0.30 in.

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