Section
4 Vibration control
4.1 General
4.1.1 Natural
frequencies are to be investigated for local unstiffened and stiffened
panels expected to be exposed to excessive structural vibrations being
induced from machinery, propulsion unit or other potential excitation
sources.
4.1.2 Where
the structural configurations are such that basic structural elements
may be modelled individually the natural frequencies may be derived
in accordance with Vol 1, Pt 6, Ch 2, 4.3 Natural frequency of plate, Vol 1, Pt 6, Ch 2, 4.4 Natural frequency of plate and stiffener combination and Vol 1, Pt 6, Ch 2, 4.5 Effect of submergence, as appropriate. Under other circumstances, finite element
analysis is to be employed to evaluate the vibration characteristics
of the structure considered.
4.2 Frequency band
4.2.1 The
natural frequency of panels is generally not to lie within a band
of ±20 per cent of a significant excitation frequency.
4.3 Natural frequency of plate
4.3.1 The
natural frequency of an homogeneous clamped plate in air is given
by the following:
|
fair
|
= |
|
where
|
= |
panel length, in metres |
|
tp
|
= |
panel thickness, in mm. |
4.4 Natural frequency of plate and stiffener combination
4.4.1 The
natural frequency of a plate stiffener of constant cross-section in
air is given by the following:
|
fair
|
= |
|
where
 b
|
= |
length of
stiffener, in metres |
|
m
|
= |
mass
per unit length of the stiffener and associated plating, in kg/m |
|
G
|
= |
shear
modulus of elasticity, in N/mm2.
|
|
A
|
= |
shear
area of stiffener, in cm2
|
|
= |
Inertia of stiffener,
in cm4
|
|
E |
= |
modulus of elasticity,
in N/mm2
|
Table 2.4.1 First mode of vibration constant
Ki
| End condition
|
Mode
|
| 1
|
2
|
3
|
4
|
5
|
| Simply
supported
|
9,92
|
—
|
—
|
—
|
—
|
| Fixed
ends
|
22,40
|
61,70
|
121,0
|
200,0
|
299,0
|
| Simple and
fixed
|
15,4
|
—
|
—
|
—
|
—
|
4.5 Effect of submergence
4.5.1 To obtain
the frequency, f
water, of a plate with one
side exposed to air and the other side exposed to a liquid, the frequency
calculated in air f
air may be modified by
the following formula:
|
f
water
|
= |
|
where
|
ρ
l
|
= |
density of the liquid, in kg/m3
|
|
ρ
p
|
= |
density of the plate, in kg/m3
|
|
κp
|
= |
|
where  , s and t
p are as
defined in Vol 1, Pt 6, Ch 2, 4.3 Natural frequency of plate 4.3.1
|
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