Comparative Analysis of the Voigt–Kelvin and Maxwell Models …
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from where we have
˜
X =
F 0
k − mω 2
+ jcω
(3)
The amplitude of the vibration of the vibratory roll with mass m emerges from
(3) as
X
V −K
0
=
m 0 r ω
2
k − mω 2
2 + c 2 ω 2
(4)
The dynamic force transmitted to the soil, formal in the complex is given by the
relation
˜
Q = k ˜
x + c ˙ ˜
x
or
˜
Q = (k + jcω) ˜
Xe
jωt
(5)
Taking into account the relation (3), we have
˜
Q = F 0
k + jcω
k − mω 2
+ jcω
(6)
The amplitude of the force transmitted (maximum transmitted force) to the soil
in the process of dynamic compaction emerges as
Q
V −K
0
= m 0 r ω
2
k 2 + c 2 ω 2
k − mω 2
2 + c 2 ω 2
(7)
It is found that for ω ω n , where ω n =
k
m
, that is for the after-resonance are
of technological functioning, it may be passed to the limit with ω → ∞, in which
case we have
(a) X
K −V
0
=
m 0 r
m
The amplitude remains constant regardless of the variation of the excitation pulse ω,
when ω ω n .
(b) Q
K −V
0
=
m 0 r
m
cω
The maximum transmitted force linearly varies with the variation of the excitation
pulse ω.