Waves in fluid and solid media 97
example will, however, be on an input mobility, not a transfer mobility (the ratio of
velocity at one point and the force at another point) as used in modal analysis. The
mobility we are using is also calculated, not measured, but this gives us the opportunity
to vary the parameters to illustrate the influence of, for example damping.
The object is a 15 mm thick glass plate of rectangular shape, simply supported
along the edges of length 1.10 metre and 1.50 metre, respectively. It is driven by a
constant force normal to the plate at a point (x,z) equal to (0.20, 0.50). The input
mobility, again using a logarithmic scale, is shown in Figure 3.23 for two values of the
loss factor η. The highest value used is not a realistic one but is used to illustrate the
influence of damping.
The thick horizontal line in the figure gives the mobility for an infinitely large plate
of the same material and thickness. It may be surprising that this mobility is independent
of frequency and at the same time is a real quantity. It should be noted that this is not
generally true; e.g. neither the input mobility at the midpoint of an infinitely long beam
nor at the end of a half-infinite beam has these characteristics.
On this horizontal line some marks have been made indicating some of the lowest
natural frequencies of the plate, five frequencies altogether. The fourth and the fifth
nearly fall together, which indicates that it is not always possible to detect the natural
frequencies from such measurement data. The bandwidth of a resonance maximum may
be larger than the distance between the natural frequencies. Several natural frequencies
may then, depending on the damping, “hide” themselves inside a resonance maximum. It
should also be remembered that one does not get any response from a certain mode
having a node, i.e. zero displacement, at the driving point.
Figure 3.23 Input point mobility of a 15 mm thick glass plate, dimensions 1.10 x 1.50 metre, for two different
loss factors. Solid horizontal line – mobility of an infinite size plate, with marks indicating the first five natural
frequencies of the finite plate.
10 20 50 100 200 500 1000 2000 5000
Frequency (Hz)-100
-90
-80
-70
-60
-50
Mobility (dB re 1m/Ns)η = 0.05
η = 0.2