Parametric Analysis of Dynamic Insulation in the Action …
371
Carrying out all operational calculations based on relations (8) and (9) it is
obtained the amplitude of the force transmitted as
Q 0 =
X 0
D
R 2 + I 2
(10)
where we have
R = −N
2 k
2 mω
2
(k + cω)
k − mω
2
− kmc
2
ω
4
k + k N − mω
2
I = N kmcω
3
cω
k − mω
2
+ N k(k + cω)
(11)
4 Transmissibility Displacement
By definition transmissibility T of movement is given by relation
T =
A
X 0
(12)
or taking into account the expression of A, we have
T (c, ω) =
N 2 k 4 + c 2 ω 2 k 2 (1 + N ) 2
D
(13)
with the representation in Fig. 4 [1, 5].
5 The Linear Viscous Dissipated Energy
The energy dissipated in the composed amortization system with the equivalent
constant c is given by the relation
W d = π cωZ
2
0v
(14)
In relation (14) we insert relation (7) and we obtain
W d (c, ω) = π X
2
0
m
2 k
2 cω
5 N
D
(15)
with representation in Fig. 5.
371
Carrying out all operational calculations based on relations (8) and (9) it is
obtained the amplitude of the force transmitted as
Q 0 =
X 0
D
R 2 + I 2
(10)
where we have
R = −N
2 k
2 mω
2
(k + cω)
k − mω
2
− kmc
2
ω
4
k + k N − mω
2
I = N kmcω
3
cω
k − mω
2
+ N k(k + cω)
(11)
4 Transmissibility Displacement
By definition transmissibility T of movement is given by relation
T =
A
X 0
(12)
or taking into account the expression of A, we have
T (c, ω) =
N 2 k 4 + c 2 ω 2 k 2 (1 + N ) 2
D
(13)
with the representation in Fig. 4 [1, 5].
5 The Linear Viscous Dissipated Energy
The energy dissipated in the composed amortization system with the equivalent
constant c is given by the relation
W d = π cωZ
2
0v
(14)
In relation (14) we insert relation (7) and we obtain
W d (c, ω) = π X
2
0
m
2 k
2 cω
5 N
D
(15)
with representation in Fig. 5.