Geotechnical Engineering

DHARM

ELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 825

where A =

P

M

o

ωαω ω ωnn

(^222) +−()2 2 ...(Eq. 20.44)
and φ = tan
()
−
−
R
S
|
T|
U
V
|
W|
1
22
α
ωω
W
n
...(Eq. 20.45)
A may also be expressed as
A =
P
MD
o
ωξn ξ
(^22222) () 14 −+ ...(Eq. 20.46)
where ξ =
ω
ωn
, the frequency ratio.
There are two kinds of excitation: constant force-amplitude excitation and quadratic
excitation.
Constant Force—Amplitude Excitation
This type is caused by an electro-magnetic vibrator, the exciting force being generated mainly
from the magnetic attraction or repulsion due to the change in intensity or direction of mag-
netic flux linking several flux-carrying elements (Fig. 20.14). The magnetic flux is produced by
passing an electric current through a winding on one part of the magnetic circuit. The result-
ant magnetomotive force is proportional to the current passing through the coil. The other
winding is placed in order to generate a force having fundamental frequency of the magnetic
circuit and to eliminate the rectification process. An electromagnetic vibrator is driven by a
frequency oscillator and power amplifier.
Armature
(laminated iron)
Electromagnetic core
(laminated iron)
Fig. 20.14 Electromagnetic vibrator
Eq. 20.46 may be rewritten as follows:
A = η 1 Ast ...(Eq. 20.47)
where η 1 =
1
() 14 −+ξξ^22 D2 2
...(Eq. 20.48)
Since Ast is a constant for given spring and excitation, amplitude of motion A is directly
proportional to η 1.