Page 472 - Industrial Power Engineering and Applications Handbook

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Figure 14.20 A typical free vibration record (sine wave) illustrating natural frequency of vibration and level of damping of an object

,- System response

Peak response
(spectral response)

Ground motion
mx” kx cx’
(Inertia (Restoring (Damping
Peak acceleration (ZPA) force) force) force)
Free body diagram of mass
Figure 14.21 A single degree of freedom system

This is an important equation that defines the behaviour
of a vibrating body under different conditions of applied
force or motion F(t). From this it can be inferred that the
and 77 = response or movement of object ‘x’ will depend upon q
2fi and cu, . q is termed the fraction of critical damping and
w,, the angular natural frequency of the system. With
77 is the fraction of the critical damping constant, then
the help of these equations, the response characteristics
-=2q,- %G of an object to a force F(t, can be determined.
C
rn
Damping characteristics
F An object can acquire the following four types of damping
and - = X” + 2 .q . W, . x’ + W: . x characteristics:
in