478
F. Scheaua
Fig. 4 Force–displacement
diagram for the pendulum
insulation system
F =
P
R cos ϕ
· u +
F f
cos ϕ
(8)
where
R—the concave surface radius;
u—displacement.
When there are small displacements on the supports, the equation of the lateral
force becomes [5]:
F =
P
R
· u + μ · P · sgn( ˙
u)
(9)
where
μ—the coefficient of friction between the two surfaces;
u—rolling velocity.
It should be noted that the normal load on the support consists of static load (P)
correlated with the effect of the vertical acceleration of the foundation ground ( ¨
u v ),
as well as the additional seismic load provided by the twisting moment ( p s ) [5]:
N = P
1 +
¨
u v
g
+
p s
P
(10)
The sliding surface radius is the essential parameter in the operation of friction
bearings and its choice influences the operating efficiency of the insulating system.
Also, the friction coefficient between the two surfaces in contact may influence
the behavior of the insulating system and the insulated structure.
The isolation system is based on the dry friction force between the components
surface in contact and develops a return force during the rolling motion on the bearing
according to the surface geometry, and the vibration period can be described by the
relation [5]:
T = 2π
R
g
(11)