Re-Shaping Hysteretic Behaviour Using Semi-Active
Resetable Device Dampers
J. Geoffrey Chase, Kerry J. Mulligan, Alexandre Gue, Thierry Alnot, Geoffrey Rodgers, John
B. Mander, and Rodney Elliott
Departments of Mechanical and Civil Engineering, University of Canterbury, Private Bag 4800, Christchurch,
New Zealand
Email: geoff.chase@canterbury.ac.nz
Bruce Deam
Leicester Steven EQC Lecturer in Earthquake Engineering, Dept of Civil Eng., Univ. of Canterbury,
Christchurch, New Zealand
Lance Cleeve and Douglas Heaton
C&M Technologies, Christchurch, New Zealand
(Corresponding Author = Dr. J. Geoffrey Chase (details above))
Keywords: Resetable Devices, Seismic Hazard, Energy Dissipation, Semi-Active Control,
Damping, Supplemental Damping, Hysteretic Behaviour
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ABSTRACT:
Semi-active dampers and actuators hold significant promise for their ability to add
supplemental damping and reduce structural response, particularly under earthquake loading.
However, to date, very little large-scale design, development or testing has been done with
these devices, limiting the knowledge of what practical obstacles may stand between theory
and successful implementation. In this research, a one fifth scale semi-active, resetable device
is designed and tested to determine the efficacy of this controllable form of supplemental
damping. Resetable devices are essentially non-linear spring elements that are able to actively
reset their rest length, releasing stored energy before it is returned to the structure, thus
creating a semi-active form of supplemental damping.
A novel device design that utilises each chamber independently, allows more flexible control
laws than previous resetable devices. It also enables better performance for large-scale
devices and structural control testing as it is better able to account for significant times to
release stored energy than previous designs. More importantly, this approach allows the
hysteretic behaviour of the structure to be actively modified by design and re-shaped to
increase damping without increasing base shear forces, a potentially important advantage for
retrofit applications.
The designed device characteristics, with air as the working fluid, are determined and a nonlinear analytical model developed. The design stiffness is 250 kN.m-1 with the prototype
having a stiffness of 185-236 kN.m-1. The peak force achieved by the prototype is in excess of
20kN at a piston displacement of 33mm. The model is experimentally validated and used to
experimentally determine the effect of the actuator in a virtual structure through an iterative,
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hybrid form of dynamic testing, avoiding the need for full structure shake table testing at this
stage of development. Hence, different semi-active control laws can be examined prior to
physical testing using the experimentally validated model and the device.
Finally, manipulation of the force-displacement hysteresis curve via innovative control laws is
demonstrated both experimentally and in simulation for three different control laws focusing
on different quadrants of the force-deflection hysteresis loop. The results for this form of
stiffness-based supplemental damping are clearly evident in significant reductions up to 60%
in displacement and acceleration response spectra, particularly for periods of 0.5-2.0 seconds,
which is the region of concern for earthquake resistant design. In addition, finite times to
release energy relative to structural or ground motion dynamics are seen to limit performance
and must therefore be accounted for in design. Overall, this research demonstrates that largescale resetable devices can be practically implemented using very simple designs to deliver
measurable supplemental damping and resistive forces, and the issues which must still be
overcome are clearly delineated.
1. INTRODUCTION
Semi-active control is emerging as an effective method of mitigating structural damage from
large environmental loads by the addition of supplemental damping. In particular, it offers
two main benefits over active control and passive solutions. First, a large power/energy
supply is not required to have a significant impact on response. Second, semi-active systems
provide the broad range of control that a tuned passive system cannot, making them better
able to respond to changes in structural behaviour due to non-linearity, damage, or
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degradation over time. Semi-active systems are also strictly dissipative and do not add energy
to the system, with the resulting supplemental damping guaranteeing controlled stability.
Semi-active devices are particularly suitable in situations where the device may not be
required to be active for extended periods of time, but may be suddenly required to produce
large forces. Because they utilise building motion inputs to generate resistive forces, their
main attribute is the ability to manage these forces and dissipate energy in a controlled, or
planned fashion. The potential of semi-active devices and control methods to mitigate damage
during seismic events is well documented (e.g. Barroso et al., 2003; Jansen and Dyke, 2000;
Yoshida and Dyke, 2004, Bobrow et al., 2000). However, most structural control research,
both active and semi-active, has been analytical with very little large scale design or
experimental validation. Given the potential of these types of devices, such design and testing
is required to determine the fundamental dynamics of these devices and their potential for
practical seismic response mitigation. The results of larger-scale testing will also better define
the potential obstacles and limitations to practical implementation.
Ideally, semi-active devices should be reliable and simple. Resetable damper devices fit these
criteria as they can be constructed with ease and utilise well understood fluids, such as air or
hydraulic oils. These attributes contrast with more mechanically and dynamically complex
smart material based semi-active devices such as electro-rheological and magneto-rheological
devices (Dyke et al, 1996; Spencer et al, 1997).
Resetable devices act as hydraulic or pneumatic springs, resisting displacement in either
direction. However, they possess the ability to release the stored spring energy at any time,
creating the semi-active aspect of these devices. Therefore, instead of altering the damping of
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the system directly, resetable devices non-linearly alter the stiffness with the stored energy
being released, rather than returned to the structure, as the compressed fluid is allowed to
revert to its initial pressure.
More specifically, resetable devices are fundamentally hydraulic or pneumatic spring
elements in which the unstretched spring length can be reset to obtain maximum energy
dissipation from the structural system (Bobrow et al. 2000). Energy is stored in the device by
compressing the working fluid or gas as the piston is displaced from its centre position. When
the piston reaches its maximum displaced position, the stored energy is also at a maximum.
At this point, the stored energy is released by discharging the air, or fluid, to the non-working
side of the device, thus resetting the un-stretched length. As the device begins moving in the
other direction it resists that motion until the next change of direction. Hence, for a sinusoidal
input the device resists motion between the maximum and minimum peaks, and resets the rest
length at these peaks. Figure 1 shows the conventional resetable device configuration, with a
valve connecting the two sides as defined in Bobrow et al. (2000). Note that this original
design assumes the stored energy and fluid can switch chambers relatively instantly,
compared to the structural motion input to the device, or significant supplemental damping
and device performance will be lost.
Prior to this research the largest capacity experimental resetable device delivered
approximately 100N and therefore offered the capability of releasing all the stored energy
effectively instantaneously relative to the structural periods being considered (Bobrow and
Jabbari, 2002). For larger devices the rate of energy dissipation may be more important as the
flow rates required for large systems to release large amounts of stored energy will potentially
be very high, and the resulting time to release all stored energy may well be significant in
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comparison to the structural response and dynamics. Failure to release all stored energy would
significantly reduce the effectiveness of the device and the supplemental damping it adds to
the structure. Therefore, more detailed models are required than previously reported to create
effective designs and to determine the true effectiveness of these devices at more realistic and
practical sizes.
Semi-active damping via resetable devices also offers the opportunity to sculpt or re-shape the
resulting structural hysteresis loop to meet design needs, as enabled by the ability to actively
control the device valve and reset times. For example, given a sinusoidal response, a typical
viscously damped, linear structure has the hysteresis loop definitions schematically shown in
Figure 2a, where the linear force deflection response is added to the circular force-deflection
response due to viscous damping to create the well-known overall hysteresis loop. A similar
effect would be seen from standard viscous orifice damper devices that are currently
marketed. Figure 2b shows the same behaviour for a simple resetable device where all stored
energy is released at the peak of each sine-wave cycle and all other motion is resisted
(Bobrow and Jabbari, 2002). With a stiff damper significant energy can be dissipated using
this semi-active form of supplemental damping. However, the resulting base-shear force is
increased due to the addition of viscous or resetable semi-active damping. If the control law
for the damper is changed such that only motion towards the zero position (from the peak
values) is resisted, the force-deflection curves that result are shown in Figure 2c. In this case,
the semi-active resetable damper force actually reduces the base-shear demand compared to
the situation shown in Figures 2a-b. As a result, the use of controllable semi-active devices
offers the opportunity to re-shape and customise the overall structural hysteretic behaviour
while also providing supplemental damping to minimise response.
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Overall, resetable device design and implementation, while offering significant promise, are
still in their infancy. This paper investigates the design, testing and analysis of a one fifth
scale resetable device using air as the working fluid. The dynamic and force characteristics of
the device are established by experimental tests exploring the response to various input
signals. In addition, the impact and efficacy of different device control laws in adding
supplemental damping is determined. Particular focus is given to the amount of time required
to dissipate large amounts of stored energy and its impact on performance, as well as the
impact of different control laws on the resulting hysteresis loop. Once characterised, a
detailed model is created and validated experimentally. Finally, the ability of this type of
device at reducing the demand on a structure during seismic events is investigated in terms of
response spectra, using the realistic, experimentally validated non-linear model created.
2. RESETABLE DEVICE DYNAMICS
Unlike previous resetable devices, the resetable device design developed in this research
eliminates the need to rapidly dissipate energy from one side of the device to the other, as in
Figure 1, by using a two-chambered design that utilises each piston side independently. This
approach treats each side of the piston as an independent chamber with its own valve and
control, as shown in Figure 3, rather than coupling them with a connecting valve. This
approach allows a wider variety of control laws to be imposed as each valve can be operated
independently allowing independent control of the pressure on each side of the piston.
For this research, air is utilised as the working fluid for simplicity and to make use of the
surrounding atmosphere as the fluid reservoir. In combination with independent valves it
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allows more time for the device pressures to equalise as resetting the valve does not require
all the compressed air to flow to the opposite chamber, as it would for the design in Figure 1.
Hence, while the opposing chamber is under compression the previously reset chamber can
release pressure over a longer time period by having its valve open. This approach would not
be feasible with the single valve design in Figure 1 as it would eliminate the ability of the
opposing chamber to store energy if the valve were still open. Hence, for the practically sized
devices presented in this research, this design has the advantage of allowing significant
amounts of energy to be stored and dissipated.
Developing equations to represent the force-displacement relationships for each chamber
enables the design space to be parameterised. More specifically, each chamber volume can be
related to the device’s piston displacement, which in turn leads to a change in pressure and
therefore resistive force of the device. Resetting the device, by opening the valve on the
compressed portion, releases the stored energy as the pressure equalises with, in the case of
air as the working fluid, the atmosphere.
Therefore, assuming air is an ideal gas, it obeys the law:
pV   c
(1)
where γ is the ratio of specific heats, c is a constant and p and V are respectively the pressure
and volume in one chamber of the device (Bobrow et al. 2000). If the piston is centred in the
device and the initial pressure p0 in both chambers with initial volumes V0, the resisting force
is defined as a function of displacement, x:
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F ( x)  ( p2  p1 ) Ac


 (V0  Ax )   (V0  Ax )  Ac
(2)
where A is the piston area. Equation (2) can be linearised and an approximate force defined:
F x   
2 A2P0
x
V0
(3)
Hence, the effective stiffness of the resetable device, k1, is readily defined:
k1 
2. A2 . .P0
V0
(4)
Similar equations can be used to model, independently, the pressure-volume status of each
chamber of the device in Figure 3. The stiffness in Equation (4) can be used to design the
device to produce a set level of force at a given displacement, or additional stiffness, for the
structure. Since, it contains the device geometry in the area and volume terms it can be used
to parameterise the design space to determine the appropriate device architecture.
3. EXPERIMENTAL DEVICE DESIGN
The device is designed for a one fifth scale, four story steel moment resisting test frame with
basic dimensions of 2.1x1.2x2.1 meters and a total seismic weight of 35.3kN as described by
Kao (1998), and is widely used in the University of Canterbury Structures Laboratory. The
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natural period of the structure is 0.6s and its structural damping approximately 5% of critical.
Given that the total actuator authority might have a reasonable value of approximately 15%
total building weight (Hunt, 2002), and assuming two actuators in the structure, a stiffness of
~250 kN.m-1 was required. This stiffness results in a force of 2.5kN developed at 10mm
displacement of the piston from its centre position, which represents a large story drift for this
structure when subjected to a large magnitude ground motion (Kao, 1998).
Trade off curves for a pneumatic-based resetable actuator with air as the working fluid show
the relationships between the fundamental design parameters. The primary parameters are the
diameter, individual chamber length, and maximum piston displacement. The tradeoffs
between these variables are shown in Figure 4 for different stiffness values. These parameters
control the stiffness of the device using Equations (2) to (4). The practical design space
(boxed) is determined by combining these curves with practical, cost, safety and ease of
handling constraints. These added constraints include ensuring the length of each chamber is
superior to the maximum likely displacement of the piston (30mm), limiting the internal
pressure to 2.5 atmospheres, keeping the weight of the device under 20kg, and the cylinder
diameter at approximately 0.2m, or less. The final design parameters selected are marked with
an “X” and are in the upper left corner of the design space shown in Figure 4.
An exploded view of the device is shown in Figure 5. The piston located inside the cylinder
has four seals, each located in a groove, to ensure minimum air movement between the two
chambers, as such movement would reduce the effective stiffness and energy dissipated by
the device. The end caps are press fitted into the cylinder and held in place by four rods. An
O-ring located between the end caps and the cylinder further ensures no leakage of air. Air is
prohibited from escaping where the piston rod passes through the end caps by two seals
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located in the end caps. An elevation view is shown in Figure 6 and the assembled prototype
in a MTS test rig is shown in Figure 7. The final critical device dimensions selected are an
internal diameter of 0.2m with a max stroke in either direction of 34.5mm from device center.
4. RESULTS
4.1 Experimental Device Characterisation
Initial tests with a sine wave piston displacement input indicate the device behaves as
expected. The peak force developed at a displacement of 10mm from the centre ranges
between 1.85 and 2.36 kN, as shown in Figure 8, resulting in a stiffness between 185 kN.m-1
and 236 kN.m-1 respectively, depending on the frequency of the input signal. Higher
frequencies produced a higher peak force for the same displacement, likely due to air losses
around the seals selected for this experimental device, as faster motion results in the piston
ring seals used engaging more effectively. The reduction in stiffness from the design value
may also be partly attributed to air loss via the valves due to valve flexibility. More
specifically, the valves chosen can open slightly at higher pressures due to flexibility of the
valve cover. Another source of error will be the difficulty in setting the piston at exact dead
centre of the device chamber for each test, creating slight deviations with changes in the air
column length to be compressed. These issues can be readily solved with improved design
choices for valves and seals in forthcoming experimental devices. Overall, the force generated
is fairly similar for each input frequency, indicating that friction effects and sealing ring
stiffnesses do not measurably impact the results.
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Some of the force generated can be attributed to friction between the seals around the piston
and the cylinder wall. This contribution is approximately 250N, as seen in Figure 9, which
shows the force-displacement plot for the device with both valves open and a sine wave input
of 10mm at 1Hz and 3Hz. The curved portions of the plot are attributed to Coulomb damping
as the air is forced through the open valves, which act as an orifice. The faster the air is forced
through the restriction the greater the resistance force, as seen in Figure 9 where the 3Hz plot
reaches a higher force. However, the effort of forcing air through the valve is observed in the
significant energy release times required relative to the input motion for some test cases.
The next step is to determine the amount of time required to dissipate the stored energy at
different device displacement levels. The input motion is sinusoidal and the valves are opened
at peak displacements, with the resulting hysteretic behaviour shown schematically in Figure
2b. The valves are held open for different periods of time to determine the impact of resetting
time on energy dissipation and supplemental damping. The force displacement curves for
different control laws, frequencies, and amplitudes of the input signal are shown in Figures 10
and 11. Deviations from the ‘ideal’ behaviour shown in Figure 2b occur due to finite energy
release times that are not effectively instantaneous with respect to the input motion, as well as
friction between the seals and the cylinder wall.
Figure 10 shows the difference between holding the valves open for different lengths of time.
The valve is opened at the maximum displacement for a 0.1 Hz sinusoidal input motion of
amplitude 20mm, and closed either 15mm from the centre (ie 5mm from the peak position) or
at the centre position (20mm from peak). The slow input frequency is used to ensure
significant periods for stored energy release in this experiment. The latter case results in a
greater stiffness and hence a higher peak load as the stored energy is fully released with the
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greater 2.5 second period the valve is open, compared to an open period of 0.63 seconds. This
result suggests that the valves should be open at all times, except during the period in which
that specific chamber’s air column is being compressed. This approach would ensure that the
maximum amount of the energy stored is dissipated.
Figure 11 shows the limits of the currently installed valves, using a 10mm amplitude
sinusoidal input motion at higher frequencies than the results in Figure 10. Note that the lower
amplitude of input, in this case, implies less total stored energy. The peak force at a frequency
of 1Hz is lower than that for 0.5Hz suggesting that the energy release time is insufficient to
release all the stored energy before the piston begins moving back in the same direction again.
For higher frequencies, larger or an increased number of valves are therefore needed to
release the air in a timely fashion. More importantly, not releasing all the stored energy
reduces the peak resistive force and hence, the supplemental damping that might be achieved.
These results can be used to determine the flow rates delivered by the current device. More
specifically, the flow rate can be found by ramping the displacement to a fixed value with the
valve closed, followed by opening the valve and measuring the time taken for the resistive
force to return to zero, which is associated with all the stored energy being released from the
initially compressed chamber. Experiments were run at 5 different displacement inputs, with
the more likely to occur middle 3 values being run twice. The data points, shown in terms of
volume as a function of release time in Figure 12, are then fit with a linear line to get an
average flow rate of approximately 29 L/sec for the device and valves designed. Note that the
volumes in Figure 12 are readily converted to deflection using the piston area of, A = 0.0324
m2. Finally, the forces and times in Figure 12 are both much larger than the relatively very
small devices in Bobrow et al. (2000). More importantly, the release times are now significant
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relative to the potential seismic input frequencies and structural response dynamics that might
be encountered.
4.2 Dynamic Model and Experimental Testing Method
Once the operating parameters of the device were understood, a detailed non-linear, analytical
model was created in Simulink™ using Equations (1)-(4) and the results obtained above in
Figures 8-12. This analytical model includes the energy release rates from Figure 12 and
models each chamber individually, while also accounting for friction, as shown in Figure 9. It
also accounts for the small forces generated when compressing an air column against an open
valve using the results in Figure 9. The device was modelled as being situated in a linear,
single degree of freedom structure to investigate the accuracy of the non-linear, analytical
device model and the impact of different valve control laws on structural energy dissipation.
Experimental verification and dynamic testing of this model involves the following steps:

Sine waves with various amplitudes and frequencies are used as the ground motion
applied to a linear single degree of freedom structure. The displacement of the
structure and force provided by the ‘virtual’ actuator model are recorded

The simulated device displacement is input as the experimental piston displacement,
and the force provided by the prototype device recorded.

Forces from the experimental test and model are then compared. Model parameters
can then be updated to better reflect any differences between the model and
simulation, and a new simulation run in the first step.
This approach allows a simple form of real-time, full-scale dynamic testing of the device with
a virtual structure. This iterative hybrid testing is enabled by the device’s repeatable
behaviour between tests, and relies on the model being able to capture the devices
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fundamental dynamics. This analysis assumes 50% additional stiffness, in comparison to the
structural model stiffness, is provided by the resetable device. The modelled structure’s
natural period is 1.4 seconds, but can be varied by modifying the mass to create response
spectra.
4.3 Experimental Verification and Re-Shaping Hysteretic Behaviour
Two forms of device control law are tested to re-shape the structural hysteretic behaviour for
this simple one degree of freedom system. The first control law shuts the appropriate valve
when the device moves away from the centre position, resisting outward motion of the
structure. This control law provides significant damping forces only in quadrants 1 and 3 of
the force deflection curve, and is denoted a “1-3 device”. The second control law resists
motion towards the centre, as shown in Figure 2c. This semi-active device control is denoted
a “2-4 device” and thus resets at zero displacement and maximum velocity. For completeness
the original control law proposed in Bobrow and Jabbari (2000) and shown in Figure 2b is
denoted a “1-4 device” as it significant provides supplemental forces and damping in all four
quadrants. The “1-4” device thus resets at peak displacement and zero velocity, contrary to
the “2-4” device.
Figure 13 shows the results for the 1-3 damper, where the model and experimental results are
overlaid for a 0.1Hz sinusoidal ground motion of 2 ms-2. Note that offsets or shifts from
centre are due to experimental results where the actuator is not exactly centred. In addition,
the forces match much better at smaller displacements and forces. Differences in peak forces
at larger displacements are due largely to leakage from the valves at higher pressures. Another
source of error in this case is due to slightly reduced stiffness delivered by the experimental
15
device in this experiment compared to what is modelled. Finally, note that the hydraulic
system running our MTS test system was not able, for unknown reasons, to provide enough
tensile force at higher loads, which may be a partial cause for some error at positive
displacements. The analytical device model is based on Equation (3), however, note the final
model is non-linear due to including the effects of friction, fluid venting times and Coulomb
damping in the model. The forces in quadrants 2 and 4 are due to Coulomb damping when
pushing air out of an open orifice as the device returns towards centreline from a sinusoidal
peak, per the results in Figure 9. Coulomb damping is represented in the model as a constant
force when the valves are open, it is incorporated to account for the difference between the
model using the equations developed and the actual results. Overall, the model is seen to be a
good representation of the physical device.
Results for the 2-4 device are shown similarly in Figure 14. The results again, match well
between the modelled and experimental devices for a single iteration of the procedure
presented, validating the fundamental models and methods presented. There is a slight shift in
the positive force direction of the results, which can be misleading in this instance, and is
attributed to imperfect centering of the device prior to testing, where only a few millimetres
off centre can have significant impact at larger displacements.
As expected, the 2-4 device is beneficial in structural control as significant additional energy
is removed from the system. The significant damping in only quadrants 2 and 4 do not result
in an increase in base shear. The latter result is more clearly evident in simulation of the
device and structure, as shown in simulation in Figure 15 where the structural damping is set
to 0% for clarity. Figure 15 shows the results of a linear model of the structure and the linear
model of the actuator develop from Equation (3) without any non-linear effects modelled. The
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equivalent result is shown in Figure 16 for the iterative hybrid test result in Figure 14, hence
the response of the actuator is non-linear. The experimental actuator results are combined
with the linear structural model response to obtain the overall response of the linear singledegree-of-freedom structure with a non-linear actuator providing supplemental damping.
Most importantly, Figures 15 and 16 both show that this semi-active resetable device
approach to supplemental damping removed the energy from the system without increasing
the base shear.
4.4 Analysis of Device Impact on Structural Response
Investigation of different control laws suggested that the force-displacement curve of the
device and hence the structure can be sculpted. To determine the impact for a wider range of
structures, displacement and acceleration response spectra for the originally proposed 1-4
device control law of Bobrow et al (2000), and the 2-4 device control law are created in
simulation using the non-linear resetable device model. The spectra are created for three
earthquake ground records that are scaled for their probability of excedance in 50 years for the
Los Angeles area, which were developed as part of the SAC project (Sommerville et al.
1997). The specific ground motions used are: Kern County 1952, Landers 1992 and Kobe
1995. These ground motions are scaled to peak ground accelerations with a 50%, 10% and
2% probability of excedance in 50 years, respectively. They are also selected to broadly cover
the range from far-field events (Kern County) to extreme near-field events (Kobe), as well as
a range of damaging magnitudes. The choice of these three earthquakes from the suites of
Sommerville et al (1997) is arbitrary and is not intended to be complete, as the goal of this
research is to demonstrate large-scale experimental testing of these devices and show their
effectiveness in re-shaping hysteretic behaviour using semi-active supplemental damping.
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Figures 17 to 19 show the three ground motion records for the 1-4 device proposed by
Bobrow et al (2000), as it is the originally suggested resetable damper control law. Each
figure shows the ground motion acceleration, acceleration response spectra and displacement
response spectra. In each case, spectra are developed for resetable devices with stiffnesses of
20%, 50% and 80% of the structural stiffness, where the structural period is varied by
modifying the mass. In each case, the greater the stiffness of the device the greater the
supplemental damping provided, and the more significant the impact for these three arbitrarily
selected earthquakes. For Kobe the large pulses that characterise this earthquake lead to large
displacements which create significant damping during this part of the motion and result in
the up to 60% reductions seen in the spectra. Finally, note that in all cases the results show
significant reduction in spectral response out to periods of approximately 2 seconds, beyond
which variable improvement is noted. However, the device design presented and the specific
device controls developed are generally seen to be effective for structural periods of concern
in earthquake resistant design, and show promise for periods of concern in wind load resistant
design.
Figures 20 to 22 are displayed similarly and show very similar results for the 2-4 device.
However, the up to 50% improvements seen are similar or slightly less than those obtained for
the 1-4 device. This result should be expected because the 2-4 device’s unique control law
adds dissipation without increasing base shear or stiffness in any way that would increase
acceleration, as was noted for 1-4 devices in non-linear structural control simulations by
Barroso et al (2003) and Hunt (2002). However, this advantage comes at the cost of reducing
the supplemental damping added to the structural hysteresis loop response (for a given
device), as shown schematically in Figures 2. As a result, the response spectra are improved
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compared to the uncontrolled, passive design case, without increasing base shear, which may
be important for some retrofit applications.
Overall, the addition of a resetable device to the structure is shown to be beneficial for a wide
range of structures. The reductions in the displacement and acceleration spectra are substantial
when large displacements occur, as large amounts of energy are dissipated by this form of
supplemental damping device. For structures with periods greater than 2 seconds less effect is
seen at some periods. However, as noted, these structures are often designed based on wind
excitation concerns rather than for ground motions.
More importantly, the 2-4 device shows that hysteretic behaviour can be sculpted or re-shaped
to meet desired requirements. This result is also illustrated experimentally for the 1-3 device
shown in Figure 13. In essence, the active control of the device valves can manage energy
storage and dissipation far more optimally than previous designs. This approach also enables
the re-shaping of structural hysteretic behaviour by design.
Resetable devices can also achieve superior performance without increasing acceleration
response, as seen in the acceleration spectra shown in Figures 17-22, which can have
significant impact on occupant and internal damage and can be important design constraints
for specific structures. In particular, the ability to add supplemental damping without
increasing base shear using a 2-4 device control law could be particularly important for retrofit applications where the foundations may not be able to handle increased shear forces.
However, significant further work needs to be done before more large-scale devices can be
designed. Foremost, among the issues to address is the need to analyse the impact of these
19
devices over larger suites of ground motions to better quantify their impact and effectiveness.
Such results could then be statistically quantified and used in current probabilistic design
methods.
5. CONCLUSIONS
This research has proven that large scale resetable devices, in this case with air as the working
fluid, are feasible. It is likely that similar results would be obtained for devices using
hydraulic fluids, with the associated increased design complexity. The peak force achieved by
the prototype device was in excess of 20kN. The contributions of friction between the piston
seals and cylinder wall are also shown to be relatively small compared to the typically
obtained values. The resulting stiffness of between 185 kN.m-1 and 236 kN.m-1. These values
are 75-95% of the designed stiffness with most differences associated with air leakage due to
less than optimal selection of valves and piston ring seals that did not perform as well as
required. Design deficiencies in this initial prototype can be readily corrected with more
robust design selections for these elements, and better performance would be expected.
Once the friction, stiffness and other non-linear effects were quantified, a non-linear model of
the device in a single degree of freedom system was developed and experimentally validated.
The iterative form of hybrid testing was develop to reduce the number and complexity of
physical tests required to determine the fundamental performance of different valve control
laws. The model also allows different sized devices to be investigated without the need to
build numerous prototypes and physically test them. Good correlation between the modelled
device and experimental results were found at one iteration and further iterations would refine
that correlation, validating the fundamental models and methods developed.
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The novel independent valve design allows more flexible control laws by utilising each
chamber independently. This independence results in the ability to manipulate the forcedisplacement hysteresis curve to obtain an optimal shape for civil structural or other
applications. This capability is not available from originally proposed resetable device designs
that link the two chambers with a single valve. One result of this manipulation is the ability to
remove energy from the system without increasing the base shear demand, as seen in the 2-4
control law and device application and results shown.
Response spectra are created for three earthquake records and show that a significant
improvement can be obtained versus the uncontrolled case, for either the 1-4 (original) or 2-4
control law and any amount of actuator stiffness relative to the structural stiffness. These
spectra show the efficacy of these devices to create more reliable structural energy
management in a format (spectra) typically used in structural engineering and design.
Finally, the device is stiffness and displacement based. Therefore, ground motion records that
result in large structural displacements, or have significant and large displacement pulses
show a greater improvement in the response spectra analysis, as the actuator is able to
dissipate more energy than when smaller motions occur. This result is common to both the 13 and 2-4 control laws, however the 2-4 control law has the benefit that it does not add to the
base shear of the structure by not adding significant force in the first and third quadrants of
the structural hysteresis curve, a potential benefit for some retrofit applications. As a result,
these devices may be particularly well suited to structures in regions of potential near-field
earthquake activity.
21
ACNOWLEDGEMENTS
This research was made possible with funding from the New Zealand Earthquake
Commission (EQC) Research Foundation Grant #EQC 03/497.
REFERENCES
Barroso, L R, Chase, J G and Hunt, S J (2003). "Resetable Smart-Dampers for Multi-Level
Seismic Hazard Mitigation of Steel Moment Frames," Journal of Structural Control, vol.
10(1), pp. 41-58.
Bobrow, J E, Jabbari, F, Thai, K (2000). “A New Approach to Shock Isolation and Vibration
Suppression Using a Resetable Actuator,” ASME Transactions on Dynamic Systems,
Measurement and Control, vol 122, pp. 570-573.
Dyke, S.J, Spencer, B.F, (1996). “Modelling and Control of Magneto-Rheological Dampers
for Seismic Response Reduction,” Smart Materials and Structures, vol 5. pp. 565-575.
Hunt, S, (2002). “Semi-Active Smart-Dampers and Resetable Actuators for Multi-Level
Seismic Hazard Mitigation of Steel Moment Resisting Frames,” Masters Thesis, Mechanical
Engineering, University of Canterbury, Christchurch.
Jansen, L M and Dyke, S J (2000). “Semiactive Control Strategies for MR Dampers:
Comparative Study,” ASCE J. of Eng. Mechanics, vol. 126(8), pp. 795-803.
Jabbari, F and Bobrow, J E (2002). “Vibration Suppression with a Resetable Device,” ASCE
J. of Eng. Mechanics, vol. 128(9), pp. 916-924.
Kao, G C, (1998). “Design and Shacking Table Tests of a Four-Storey Miniature Structure
Built With Replaceable Plastic Hinges,” Masters Thesis, Civil Engineering, University of
Canterbury, Christchurch.
Sommerville, P, Smith, N, Punyamurthula, S, and Sun, J, (1997). "Development of Ground
Motion Time Histories for Phase II of the FEMA/SAC Steel Project." SAC Background
Document Report No. SAC/BD-97/04.
Spencer, B F, Dyke, S J, Sain, M K, Carlson, J, (1997). “Phenomenological Model for
Magneto-Rheological Dampers,” ASCE J. of Eng. Mechanics, vol 123, pp. 230-238.
Yoshida, O and Dyke, S J, (2004). “Seismic Control of a Nonlinear Benchmark Building
Using Smart Dampers,” ASCE J. of Eng. Mechanics, vol 130(4), pp. 386-392.
22
Valve
k0
Mass
Figure 1: Schematic of a single-valve, semi-active resetable actuator attached to a single
degree of freedom system.
23
F
a)
δ
F
F
FS
1
4
+
δ
=
δ
3
b)
F
δ
c)
F
+
FS
δ
δ
=
F
+
2
F
F
FS
FB>FS
δ
F
δ
FB>FS
=
FB=FS
δ
Figure 2: Schematic representation of hysteretic behaviour for a) added or structural viscous
damping, b) a 1-4 resetable device that resists motion between peaks before resetting, and c) a
2-4 resetable device that resists motion only toward equilibrium and adds damping only in the
2nd and 4th quadrants of the force-deflection plot. The quadrants are labelled in the first panel,
and FB is the total base shear while FS is the base shear for a linear, undamped structure. FB >
FS indicates an increase in base shear due to the damping added.
24
Valve
Piston
Cylinder
Figure 3: Schematic of independent chamber design. Each valve vents to atmosphere for a
pneumatic, or air-based device, or to a separate set of plumbing for a hydraulic fluid-based
device.
25
D=f(L0) for a displacement of 20mm
0.700
L0 min
L0 max
250kN/m
0.600
diameter (m)
0.500
125kN/m
0.400
50kN/m
0.300
25kN/m
0.200
X
Max diameter
0.100
0.000
0.000
0.100
0.200
0.300
0.400
Lo (m)
Figure 4: Tradeoff curve showing the relationship between the diameter and initial chamber
length of the device for different stiffness values assuming a maximum piston displacement of
20mm. Each line represents a different stiffness value.
26
End Cap
Seal
Cylinder
Piston
Figure 5: Exploded view of prototype indication components.
27
Figure 6: Elevation view and basic dimensions.
28
Valve and valve controller
Test
Jig
Resetable
Device
Test
Machine
Figure 7: Prototype device in test rig.
29
Peak-force at 3Hz teflon seal and 2 diesel rings,34.5mm to centre
22
1 Hz
3 Hz
5 Hz
20
18
Force (kN)
16
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
Piston Displacement from Centre Position (mm)
35
Figure 8: Peak force versus displacement for different input frequencies.
30
2000
3 Hz
1500
Force (N)
1000
1 Hz
500
0
-500
-1000
-1500
-2000
-15
-10
-5
0
5
10
Piston Displacement from Centre Position (mm)
15
Figure 9: Force versus displacement with both valves open, indicates force due to friction
between the seals and cylinder.
31
6000
4000
Force (N)
2000
Valve
opened
peakdisplacment,
displacement,
Valve
opened
at at
peak
closed
at centre
position
closed
at centre
postion
Valve closed
0
-2000
-4000
Valve opened
opened atatpeak
Valve
peakdisplacement,
position,
closed
at
15mm
from
centre
position
closed at 15mm from centre
postion
Valve opened
-6000
-30
-20
-10
0
10
20
Piston Displacement from Centre Position (mm)
30
Figure 10: Load versus displacement for different control laws for a 0.1Hz, 20mm amplitude
sinusoidal displacement input signal.
32
4000
3000
Force (N)
2000
1.0Hz
1.0Hz
Valveopened
openedatatpeak
peak
displacment,
Valve
displacement,
closedatat5mm
5mmfrom
from
centre
position
closed
centre
position
0.1Hz
Valve opened at 8.5 mm (after peak),
closed at centre position
1000
0
-1000
-2000
-3000
-4000
-15
0.5Hz
0.5Hz
Valve
at peak
peakdisplacement,
displacment,
Valve opened
opened at
closed
at
5mm
from
centre
position
closed at 5mm from centre position
-10
-5
0
5
10
Piston Displacement from Centre Position (mm)
15
Figure 11: Force vs displacement for a 10mm displacement signal at various frequencies and
two control laws.
33
-3
3
Chamber Volume prior to opening valve )(m
3.5
x 10
3
Slope = 29 L.s-1
2.5
2
1.5
1
0.5
0
0
0.02
0.04
0.06
time (sec)
0.08
0.1
Figure 12: Time to release energy from device depends on chamber volume prior to release.
Circles show measured data and the line the fitted curve to the experimental data.
34
4000
Model
3000
Force (N)
2000
1000
0
-1000
Experiment
-2000
-3000
-15
-10
-5
0
5
10
Piston Displacement from Centre Position (mm)
15
Figure 13: Force-displacement curve for actuator in a single degree of freedom structure with
1-3 control law showing showing both the analytical model prediction and experimental
result. Ground motion is a 2 m.s-2 sine wave of frequency 0.1Hz.
35
2500
2000
Force (N)
1500
Experiment
1000
500
0
-500
-1000
-1500
-2000
-20
Model
-15
-10
-5
0
5
10
Piston Displacement from Centre Position (mm)
15
Figure 14: Force-displacement curve for actuator in a single degree of freedom structure with
2-4 control law showing both the analytical model prediction and experimental result. Ground
motion is a 2 m.s-2 sine wave of frequency 0.1Hz.
36
Force (N)
2
x 10
4
0
Force (N)
-2
-0.5 4
x 10
1
0
Actuator
0.5
0
Combined
0.5
0
-1
-0.5 4
x 10
2
Force (N)
Structure only
0
-2
-0.5
0
Displacement (m)
0.5
Figure 15: Hysteresis loops for the simulated uncontrolled structure, simulated semi-active
actuator using the linear model developed from Equation (3) and the combination (linear
structure and modelled device).
37
Figure 16: Hysteresis loops for the simulated uncontrolled linear single-degree-of-freedom
structure, experimental, hence non-linear, semi-active 2-4 device from Figure 14, and their
combination. Note that the peak forces in the first and third panels are the same.
38
2
0
2
(m/s)
Ground acceleration
(m/s2)
Ground Acceleration
4
-2
-4
0
10
20
30
40
time (sec)
50
60
70
0.66
Uncontrolled
20% added stiffness
50% added stiffness
80% added stiffness
0.55
0.33
Sa
Sa
(g)
0.44
0.22
0.11
00
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.4
Sd
(m)
Sd
0.3
0.2
0.1
0
Figure 17: 1-4 device control law response spectra for Kern County 1952. Structural damping
of 5% is used.
39
2
2
)
(m/s
Ground acceleration
2
)
Ground (m/s
Acceleration
4
0
-2
-4
0
10
20
30
40
time (sec)
50
60
70
1.2
12
Uncontrolled
20% added stiffness
50% added stiffness
80% added stiffness
1.0
10
Sa
Sa
(g)
0.88
0.66
0.44
0.22
00
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
3.5
4
4.5
5
period (sec)
1.5
Sd
(m)
Sd
1
0.5
0
0.5
1
1.5
2
2.5
period (sec)
Figure 18: 1-4 device control law response spectra for Landers 1992. Structural damping of
5% is used.
40
Ground acceleration
Ground Acceleration
2
(m/s
)
2
20
10
(m/s )
0
-10
-20
0
10
20
30
time (sec)
40
50
60
40
4.0
Sa
Sa
(g)
30
3.0
20
2.0
1.0
10
00
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
1
Sd
(m)
Sd
0.8
0.6
0.4
0.2
0
Figure 19: 1-4 device control law response spectra for Kobe 1995. Structural damping of 5%
is used.
41
2
2
(m/s)
Ground acceleration
(m/s2)
Ground Acceleration
4
0
-2
-4
0
10
20
30
40
time (sec)
50
60
70
0.66
Uncontrolled
20% added stiffness
50% added stiffness
80% added stiffness
0.55
Sa
Sa
(g)
0.44
0.33
2
0.2
1
0.1
0
0
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.4
Sd
Sd
(m)
0.3
0.2
0.1
0
Figure 20: 2-4 device control law response spectra for Kern County 1952. Structural damping
of 5% is used.
42
2
2
(m/s )
Ground Acceleration
Ground acceleration
(m/s2)
4
0
-2
-4
0
10
20
30
40
time (sec)
50
60
70
10
1.0
Uncontrolled
20% added stiffness
50% added stiffness
80% added stiffness
0.88
Sa
Sa
(g)
0.66
0.44
0.22
00 0
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
1
Sd
Sd
(m)
1.5
0.5
0
0
Figure 21: 2-4 device control law response spectra for Landers 1992. Structural damping of
5% is used.
43
10
0
2
(m/s)
Ground Acceleration
Ground acceleration
(m/s2)
20
-10
-20
0
10
20
30
time (sec)
40
50
40
4.0
Uncontrolled
20% added stiffness
50% added stiffness
80% added stiffness
Sa
Sa
(g)
30
3.0
20
2.0
1.0
10
00 0
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
0.5
1
1.5
2
2.5
period (sec)
3
3.5
4
4.5
5
1
Sd
(m)
Sd
0.8
0.6
0.4
0.2
0
0
Figure 22: 2-4 device control law response spectra for Kobe 1995. Structural damping of 5%
is used.
44