Page 294 - Introduction to Naval Architecture

VIBRATION, NOISE AND SHOCK 279

Figure 11,1 Magnification factor
displacement to the static displacement is termed the magnification
factor, Q. Q is given by:

Curves of magnification factor can be plotted against tuning factor for
a range damping coefficients as in Figure 11.1. At small values of A, Q
tends to unity and at very large values it tends to zero. In between these
extremes the response builds up to a maximum value which is higher
the lower the damping coefficient. If the damping were zero the
response would be infinite. For lighdy damped systems the maximum
displacement occurs very close to the system's natural frequency and
the tuning factor can be taken as unity. Where the frequency of the
applied force is equal to the system's natural frequency it is said that
there is resonance. It is necessary to keep the forcing frequency and
natural frequency well separated if large amplitude vibrations are to be
1
avoided. At resonance the expression for the phase angle gives y = tan"
oo, giving a phase lag of 90°.
In endeavouring to avoid resonance it is important to remember that
many systems have several natural frequencies associated with different
deflection profiles or modes of vibration. An example is a vibrating beam
that has many modes, the first three of which are shown in Figure 11.2.
All these modes will be excited and the overall response may show more
than one resonance peak.

Figure 11.2 Vibration modes