Negative stiffness device and method
Negative stiffness systems and methods for seismic protection of a structure is described. A system can include a negative stiffness device having a first linkage pivotably connected to an anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point. The negative stiffness device can include a spring having a first end operably coupled to the anchor frame and a second end operably coupled to a movement frame. In a rest state, the spring can be compressed to exert a preload force to the first linkage and the anchor frame and not displace the first linkage and the movement frame. In an engaged state, the spring can be configured to apply a force to the first linkage such that the movement frame is displaced in a same lateral direction of a seismic load. The spring force can be amplified by the first linkage.
1. A negative stiffness system for seismic protection of a structure, comprising:
an anchor frame and a movement frame, the movement frame being laterally translatable relative to the anchor frame;
a first negative stiffness device, including:
a first linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a first spring having a first end operably coupled to the anchor frame and a second end operably coupled to the movement frame, the first spring having a spring force;
wherein in a rest state, the first spring is compressed to exert a preload force to the first linkage and the anchor frame and not displace the first linkage and the movement frame;
wherein in an engaged state, the first spring is configured to apply a force to the first linkage such that the movement frame is displaced in a same lateral direction of a seismic load; and
wherein the first spring force is amplified by the first linkage when the frame is laterally displaced to an amplification point; and
at least one additional negative stiffness device, each additional negative stiffness device including:
a second linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a second spring having a first end operably coupled to the first linkage of the first negative stiffness device and a second end operably coupled to the second linkage, the second spring having a second spring force;
wherein in a rest state, the second spring is compressed to exert a preload force to the first linkage and the anchor frame and not displace the first linkage and the movement frame;
wherein in an engaged state, the second spring is configured to apply a second force to the first linkage of the first negative stiffness device such that the movement frame is displaced in the same lateral direction of the seismic load; and
wherein the second spring force is amplified by the first linkage when the frame is laterally displaced to the amplification point;
wherein each of the first spring and the second spring are arranged to provide a cumulative, positive force to displace the movement frame in the same lateral direction of the seismic load.
2. The negative stiffness system of claim 1 , wherein in the rest state, the first spring and the second spring of the at least one additional negative stiffness device are arranged in series.
3. The negative stiffness system of claim 2 , wherein in the engaged state, the first linkage of the first negative stiffness device, the second linkage of the at least one additional negative stiffness device, and the third linkage of the first negative stiffness device are configured to pivot about the anchor frame in unison.
4. The negative stiffness system of claim 1 , wherein the negative stiffness system has a force-displacement relation that multiples according to a total number of springs in the negative stiffness system, the total number of springs including the first spring of the first negative stiffness device and the second spring of the at least one additional negative stiffness device.
5. The negative stiffness system of claim 4 , wherein in the engaged state, the first linkage of the first negative stiffness device, the second linkage of the at least one additional negative stiffness device, and the third linkage of the first negative stiffness device are configured to rotate relative to the anchor frame in unison.
6. The negative stiffness system of claim 5 , wherein in the engaged state, the first spring and the second spring are configured to rotate relative to the anchor frame in unison.
7. The negative stiffness system of claim 4 ,
wherein the negative stiffness system has a force-displacement relationship expressed by:
F
Brace
=
-
2
n
s
P
i
n
l
1
l
2
(
2
l
p
l
1
l
2
+
1
l
2
)
u
wherein:
F Brace is the force-displacement relationship,
n s is the total number of springs in the negative stiffness system,
P in is preload force of each of the total number of springs,
u is resultant displacement distance of the movement frame relative to the anchor frame,
l 1 is length between the second end of the second spring and the first pivot point of the second linkage,
l 2 is length between the first pivot point of the second linkage and the second pivot point of the second linkage, and
l p is length of the spring.
8. The negative stiffness system of claim 1 , wherein the first negative stiffness device further comprises a third linkage pivotably connected to the anchor frame and pivotably connected the movement frame; and
wherein the first end of the first spring of the first negative stiffness device is pivotably connected to the first linkage and the second end of the first spring of the first negative stiffness device is pivotably connected to the third linkage.
9. The negative stiffness system of claim 8 , wherein in the engaged state, the first linkage of the first negative stiffness device, the second linkage of the at least one additional negative stiffness device, and the third linkage of the first negative stiffness device are configured to pivot about the anchor frame in unison.
10. The negative stiffness system of claim 1 , further comprising at least one gap spring assembly configured to delay engagement of the first spring and the second spring by a predetermined lateral displacement.
11. The negative stiffness system of claim 10 , wherein the gap spring assembly is attached between the movement frame and the anchor frame.
12. The negative stiffness system of claim 10 , wherein the gap spring assembly is attached between the second pivot point of the second linkage and the first pivot point of the first linkage.
13. The negative stiffness system of claim 10 , wherein the gap spring assembly includes an adjustment mechanism configured to adjust the predetermined lateral displacement.
14. The negative stiffness device of claim 1 , further comprising a first gap spring assembly and a second gap spring assembly configured to delay engagement of the second spring by a predetermined lateral displacement;
wherein the first gap spring assembly is attached between the second pivot point of the second linkage and the first pivot point of the first linkage; and
wherein the second gap spring assembly is attached between the first pivot point of the second linkage and the second pivot point of the first linkage.
15. The negative stiffness system of claim 1 , further comprising at least one damping device configured to reduce lateral translation of the movement frame.
16. The negative stiffness system of claim 1 , wherein after an initial engaged state, the lateral force increases as the movement frame is displaced in the lateral direction to a peak engaged state;
wherein after the peak engaged state, the lateral force decreases as the movement frame continues to be displaced in the lateral direction.
17. The negative stiffness device of claim 16 , wherein lateral displacements between the initial engaged state and the peak engaged state the negative stiffness device exerts a negative stiffness, and in lateral displacements above the peak engaged state, the negative stiffness device exerts a positive stiffness.
18. A negative stiffness system for seismic protection of a structure, comprising:
an anchor frame and a movement frame, the movement frame being laterally translatable relative to the anchor frame;
a first negative stiffness device, including:
a first linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a first spring having a first end operably coupled to the anchor frame and a second end operably coupled to the movement frame, the first spring having a spring force;
wherein in a rest state, the first spring is compressed to exert a preload force to the first linkage and the anchor frame and not displace the first linkage and the movement frame;
wherein in an engaged state, the first spring is configured to apply a force to the first linkage such that the movement frame is displaced in a same lateral direction of a seismic load; and
wherein the spring force is amplified by the first linkage when the frame is laterally displaced to an amplification point
at least one additional negative stiffness device, each additional negative stiffness device including:
a second linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a second spring having a first end operably coupled to the first linkage of the first negative stiffness device and a second end operably coupled to the second linkage, the second spring having a second spring force;
wherein in a rest state, the second spring is compressed to exert a preload force to the first linkage and the anchor frame and not displace the first linkage and the movement frame;
wherein in an engaged state, the second spring is configured to apply a second force to the first linkage of the first negative stiffness device such that the movement frame is displaced in the same lateral direction of the seismic load; and
wherein the second spring force is amplified by the first linkage when the frame is laterally displaced to the amplification point;
a first gap spring assembly and a second gap spring assembly configured to delay engagement of the second spring by a predetermined lateral displacement;
wherein the first gap spring assembly is attached between the second pivot point of the second linkage and the first pivot point of the first linkage; and
wherein the second gap spring assembly is attached between the first pivot point of the second linkage and the second pivot point of the first linkage;
wherein in the engaged state, the first spring and the second spring are configured to rotate relative to the anchor frame in unison;
wherein each of the first spring and the second spring are arranged to provide a cumulative, positive force to displace the movement frame in the same lateral direction of the seismic load.
19. The negative stiffness system of claim 18 , wherein the anchor frame and the movement frame are attached to a structure.
20. A negative stiffness system for seismic protection of a structure, comprising:
an anchor frame and a movement frame, the movement frame being translatable relative to the anchor frame;
a first negative stiffness device, including:
a first linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a first spring having a spring force;
wherein in a rest state, the first spring is compressed to exert a preload force to the first linkage and the anchor frame;
wherein in an engaged state, the first spring is configured to apply a force to the first linkage such that the movement frame is displaced in a same lateral direction of a seismic load;
a second negative stiffness device including:
a second linkage pivotably connected to the anchor frame at a first pivot point and pivotably connected the movement frame at a second pivot point;
a second spring having a second spring force;
wherein in a rest state, the second spring is compressed to exert a preload force to the first linkage and the anchor frame;
wherein in an engaged state, the second spring is configured to apply a second force to the first linkage of the first negative stiffness device such that the movement frame is displaced in the same lateral direction of the seismic load; and
wherein each of the first spring and the second spring are arranged to provide a cumulative, positive force to displace the movement frame in the same lateral direction of the seismic load.