Dynamic Characteristics of a Novel Right-Angle Viscoelastic Damper (RVD) Using Polyurethane Damping Materials

Excessive plastic deformation may occur at the beam-column joints under seismic action and lead to connection failure, increasing the possibility of collapse of the entire frame structure. In order to improve the seismic performance of assembled steel structure joints, a right-angle viscoelastic joint damper with polyurethane as the core energy dissipation material is proposed in this paper. First, the temperature scanning tests of polyurethane materials were carried out based on the dynamic mechanical analysis method. Second, the dynamic mechanical test and numerical simulation analysis of the designed right-angle viscoelastic damper were performed to reveal the dynamic energy dissipation characteristics of the right-angle damper. Finally, the dynamic time-history damping analysis was performed on the steel frame structure equipped with RVDs. Te results show that the TA value of polyurethane material reached its peak at 2.0Hz, which is the ideal frequency for the material’s damping ability. Te right-angle damper made of polyurethane material has a softening nonlinear characteristic, and the peak value of the loss factor was obtained at 2.0Hz, which is consistent with the results of the dynamic performance of the polyurethane material. Te numerical simulation results demonstrate that stress on the steel plates and viscoelastic layers is reasonable. When the excitation level did not exceed 9mm displacement amplitude, the energy input to the damper was dissipated by polyurethane, and the steel plates never showed plastic deformation. Te time-history analysis of the steel structure shows that the dampers designed in this paper have a good control efect on the interstory displacement, acceleration, and interstory shear force of the structure. Te research results lay the necessary foundation for the engineering application of polyurethane materials in the feld of beam-column joints vibration damping.


Introduction
Te assembled steel structure has greater advantages in development and good application prospects, but its beamcolumn joints have sufered signifcant damage in successive earthquakes [1,2].Te mechanical properties of the beamcolumn joints play a crucial role in the safety and integrity of the entire frame system [3][4][5][6][7].Based on the concept of passive control, the method of setting viscoelastic dampers at beam-column joints can provide additional stifness and additional damping to the structure.Te joint damper can assist the structure in forming an acceptable form of "strong joints and weak components" to better safeguard the global stability of the frame structure under earthquake action [8,9].In addition to ground motion, viscoelastic dampers also have excellent control efects on wind-induced vibration [10].Te passive damper also has a positive impact on the resilience of the building [11,12].
Te joint dampers include metal joint dampers and sector lead viscoelastic dampers, among which the sector lead viscoelastic dampers have been studied more.Wu et al. [13] designed and fabricated the sector lead viscoelastic damper (SLVD) and found that the shear modulus of the rubber and the strain amplitude had some infuence on the SLVD performance.With the increase of the strain amplitude, the energy dissipation coefcient and the equivalent viscous damping ratio increased and then decreased; with the increase of rubber's shear modulus, the initial stifness, postyield stifness, and equivalent stifness increased, but the energy dissipation coefcient and equivalent viscous damping ratio decreased, and the loading frequency had a small efect on the performance of this damper.Wu et al. [14,15] studied the performance of a seismic device with the joint SLVD and analyzed the efects of diferent strain amplitudes, loading frequencies, and shear modulus of the rubber on the performance of the damper.Zhu et al. [16] designed and analyzed the frame structure equipped with the SLVD from the view of stifness, and the theoretical method for the design of dampers was given.Xu et al. [17] investigated the efect of the number and diameter of lead cores on the performance of the SLVD, and the results showed that the energy dissipation coefcient and equivalent damping ratio of the dampers increased with the increase of the number and diameter of lead cores.But Zhang et al. [18] conducted a destructive damaged retroftting study on an RC frame equipped with the SLVD and found that the thickness of viscoelastic materials and the diameter of lead cores contributed less to the improvement of seismic performance, while the efective radius of the sector provided a larger contribution.
According to the aforementioned studies, the beamcolumn joints of the joint viscoelastic damper have a problem with small corner deformation [19].Additionally, during the manufacturing process, the shape of the damper is curved, and there are numerous mold parts for making components, up to 20 diferent types [20].In order to fully utilizing the energy dissipation capability of the damper, this paper proposes the right-angle viscoelastic damper, which has a relatively simple structure (the structural layout is shown in Figure 1).As can be seen from the fgure, the damper is bolted to the armpit of the beam and column, which not only has the advantages of small size and does not afect the use of space but also can play a role in fxing the frame beam when installing the assembled beam structure.
Te vibration reduction mechanism of the damper is that under the horizontal action of the earthquake, the bending deformation of the beam at the joint causes the rotation of the frame beam-column joint, and the rotation can cause the steel plates of the damper connected to the beam and column, respectively, to rotate and displace, which drives the material layers of the right-angle damper to shear deformation to achieve energy dissipation.When damage occurs to the damper, the overall damage to the structure does not develop excessively, although the function of the damper will be afected or even destroyed to some extent.Te expected function of the structure can still be restored after the repair under reasonable technical and economic conditions.
As a typical representative of polymer products, polyurethane has characteristics that fall in between those of rubber and plastic.Its intermolecular force is strong, and the biggest characteristic of polyurethane is that it still maintains elasticity under high hardness, coupled with good abrasion resistance, oil resistance, low-temperature resistance, ozone aging resistance, and other properties.Terefore, the material has a wide range of applied research in the feld of damping materials [21,22].From the microscopic point of view, polyurethane has good damping and mechanical properties, [23] which is related to its main chain containing both soft and hard segments.Te two segments determine diferent properties.Te soft and hard segments produce diferent movement responses to external forces, which can cause interfacial frictions, resulting in energy consumption [24].
Terefore, a right-angle viscoelastic joint damper with polyurethane as the core energy-dissipating material was designed in this paper.First, temperature scanning performance tests were conducted on polyurethane materials to derive the variation patterns of loss factor, shear modulus, and loss modulus with the temperature at diferent frequencies of the materials.Second, dynamic performance tests were carried out on right-angle viscoelastic dampers to investigate the displacement dependence and frequency dependence of the dynamic mechanical performance parameters of the dampers.Furthermore, the experimental results of the damper were verifed by numerical simulation, and the distribution of stress and energy dissipation conditions of the damper was discussed.Finally, for one steel frame damping structure, the comparative seismic response analysis was conducted to explore the damping efect of the RVD damping system.

Dynamic Thermodynamic Testing of Polyurethane Rubber
In order to improve the accuracy of the temperature dependence, DMA tests were frst conducted on the polyurethane material used in the damper.Te curves of storage modulus E′, loss modulus E″, and loss factor tan δ versus time for polyurethane materials are shown in Figure 2. Figures 2(a)-2(d) represent the curves at 0.5, 1.0, 1.5, and 2.0 Hz, respectively.It can be seen from the fgure that the performance of polyurethane materials is stable, and its loss modulus and loss factor both tend to increase and then decrease with the increase in temperature, while the storage modulus gradually decreases with the increase in temperature.Te loss factor achieves a maximum value of 0.62 at 0.5 Hz operating conditions.
Te most scientifc method to characterize the damping performance of the material is to use the value of the integrated area of the material loss factor curve over temperature tanδ area, namely TA value, as the damping evaluation index.Te formula of calculation is shown as follows [25]: where E′ G and E′ R refer to the loss modulus value of the glassy state and the loss modulus value of the rubber state, respectively; T G and T R refer to the minimum value of the glass transition temperature and the maximum value of the rubber state transition temperature, respectively; R refers to polymer gas constant; (E a ) avg refers to average activation energy during relaxation.Te curves of the damping performance parameters of the polyurethane material with the loading frequency are given in Figures 3(a) and 3(b), including the TA value, the peak loss factor (tanδ max ), the wide damping temperature range (i.e., the temperature interval ΔT 0.5 where the loss factor is greater than 0.5), and the temperature of glass transition peak T g .As can be seen from the fgure, ΔT 0.5 decreases frst and then increases with the increase of frequency and reaches its maximum value at 0.5 Hz while the temperature of glass transition peak T g increases and then decreases with the increase of frequency.Te TA value increases gradually with the increase of frequency and reaches the maximum value of 28.2 °C when the loading frequency is 2.0 Hz, which is the best frequency to play the damping performance in the material tests.Te variation trend of the material damping properties with temperature can be clearly derived from the temperature scanning curve.
Due to the structural peculiarity that the loading end and fxed end of the designed damper are not in the same straight line, the loading device requires a special design.Te loader is a servo actuator (MTS) with a loading capacity of 1000 kN.A right-angle steel plate was placed on the test bench, and it was fxed to the test bench by bolts.Te fxed end of the RVD was fastened on the vertical surface of the right-angle steel plate by the steel plate for connection, and the shear end was connected to the MTS machine by a steel rod.Te threedimensional view of the loading device, the actual damper, and the view of the actual loading device are shown in Figures 4(b)-4(d), respectively.
As listed in Table 1, there are sixteen loading conditions in total.Five laps were loaded for each working condition, and the hysteresis curve of the third lap was taken as the calculated mechanical property index curve.

Force-Displacement Hysteresis Curves of the Right-Angle
Damper.Te damper test was conducted at room temperature (the feld measurement temperature was 21 °C), and the hysteresis curves obtained according to the loading scheme in Table 2 are shown in Figure 5. Figures 5(a)-5(d) show the force-displacement hysteresis curves at frequencies of 0.5, 1.0, 1.5, and 2.0 Hz for displacement amplitudes of 1.2, 3, 6, and 9 mm, respectively.It can be seen that the hysteresis curves for all displacement conditions are elliptical, smooth, and relatively full, characterized by the fact that the maximum damping force and the maximum deformation do not occur simultaneously due to the viscous resistance of the right-angle damper, and there is a certain phase diference.Te shape of the hysteresis loop varies with the displacement amplitude, and the hysteresis characteristics of the right-angle damper show nonlinear feature at this time.Te slope of the hysteresis curves decreases with the increase of the displacement amplitude for all frequency conditions, indicating that the stifness of the damper also tends to decrease with increasing displacement amplitude.In summary, it can be seen that the right-angle damper made of polyurethane materials has softening nonlinear characteristics.

Frequency Dependence of Hysteresis Curves.
Figures 6(a)-6(d) show the frequency dependence of hysteresis curves for the four displacement conditions (1.2 mm, 3 mm, 6 mm, and 9 mm), respectively.As can be seen from the fgure, when the displacement amplitude is 1.2 and 3 mm, the slope of the hysteresis curve shows an increasing trend with the increase of frequency, while the slope of the 3 mm displacement amplitude working condition has a smaller increase with the increase of frequency.Te four frequency curves overlap with similar slopes at the 6 mm displacement amplitude working condition.At the 9 mm displacement condition, the slope of the curve tends to decrease as the frequency increases.Te frequency dependence analysis under the four displacement conditions shows that the slope of the curve tends to increase from upward to downward as the displacement increases.Te frequency dependence is most obvious at 1.2 mm displacement amplitude working condition and least obvious at 6 mm.

Analysis of Dynamic Characteristic Index
A series of mechanical parameters of right-angle dampers were calculated from the hysteresis curve sets derived from the tests.

Maximum
Damping Force F max .Figure 7 shows the displacement and frequency dependence analysis of F max .From Figure 7(a), it can be seen that F max shows a trend of increasing and then decreasing with the increase of displacement at all four frequencies.F max for all frequencies except 0.5 Hz reaches its maximum value at 6 mm displacement.
From Figure 7(b), it can be seen that F max increases with increasing frequency at the displacement amplitudes of 1.2 and 3 mm, while at 9 mm displacement, F max decreases with the increase of frequency.Te trend of F max variation is not signifcant at the displacement amplitude of 6 mm.Te maximum value of 14.1 kN is obtained at 6 mm displacement amplitude and 1.0 Hz frequency in all operating conditions.

Storage Stifness K′ d.
Te storage stifness is related to the ability of the damper in terms of energy conversion, and the displacement dependence and frequency dependence of    the storage stifness are shown in Figure 8. Figure 8(a) shows that the storage stifness tends to decrease with the increase of displacement amplitude at all frequencies, and the four curves vary more closely.Te value of maximum stored stifness is obtained at the displacement amplitude of 1.2 mm and loading frequency of 1.5 Hz, which is 4.2 kN/mm.From the diagrams of frequency dependence shown in Figure 8(b), it can be seen that the other four variation curves are approximately horizontal except for the larger rise at the displacement of 1.2 mm.

Loss Stifness K″ d.
Te loss stifness K″ d refects the energy loss performance of the damper, and its dependence analysis graph is shown in Figure 9. From the displacement dependence analysis graph in Figure 9(a), it can be seen that the variation law of the displacement dependence is similar to the law of the storage stifness, which has the overall monotonic decreasing variation.Te maximum value is obtained at the displacement amplitude of 1.2 mm and loading frequency of 2.0 Hz, which is 2.2 kN/mm.From Figure 9(b), it can be seen that K″ d increases with increasing   Structural Control and Health Monitoring 4.5.Shear Modulus G′ and G″.Te shear modulus includes shear storage modulus and shear loss modulus, which are related to the storage and loss stifnesses as well as the thickness and shear area of viscoelastic materials, so their variation laws are highly similar to the storage and loss stifnesses, respectively.
For the shear storage modulus G′, as shown in Figure 11(a), the curves are monotonically decreasing with increasing displacement, and the maximum value of 1.3 MPa is obtained at the displacement of 1.2 mm and the frequency of 1.5 Hz.Te frequency dependence of the shear storage modulus as shown in Figure 11(b) changes in the same way as the storage stifness.For the shear loss modulus G″, as shown in Figures 12(a) and 12(b), the variation laws of the displacement-dependence and frequency-dependence curves are the same as the loss stifness, and the maximum value of 0.7 MPa is obtained at the displacement of 1.2 mm and the frequency of 2.0 Hz.

Loss Factor η.
Te loss factor is an important parameter indicating the energy dissipation capacity of the damper, and the loss factor η dependence analysis diagrams are shown in  Figures 13(a) and 13(b).From Figure 13(a), all curves decrease with the increase of displacement amplitude.Te maximum loss factor is 0.55 when the frequency is 2.0 Hz, and the displacement amplitude is 1.2 mm.

Numerical Analysis with ABAQUS
In order to investigate the stress and energy dissipation mechanism inside the right-angle type damper steel plate and polyurethane, the ABAQUS refned fnite element numerical analysis of the test damper was carried out in this thesis.

Geometric Modeling and Meshing.
Te steel plate and damping material of the damper were meshed, respectively.Figure 14(a) shows the model geometry of the damper.As shown in Figure 14(b), the approximate global sizes are 4 mm and 5 mm for the restrained and shear steel plates, respectively, and the approximate global size for the rubber is 2 mm.In order to make the calculation results more accurate and reasonable, the steel plate adopted the C3D8R meshing element type, and the damping material adopted the C3D8H meshing element type.Structural Control and Health Monitoring 5.2.Properties of the Materials.Te numerical simulation not only studies the change of energy dissipation of the damper but also explores whether plastic energy dissipation occurs in the steel plate, so the plastic characteristics are still defned on the basis of the defned elastic parameters.Te Young's modulus and Poisson's ratio of steel plates were taken as 2.06 × 10 5 MPa and 0.3, respectively.Te plastic parameters were defned in ABAQUS in terms of yield stress and plastic strain, as listed in Table 2, where i refers to the ith set of data that respond to the constitutive relation of the material.
For polyurethane materials, it was defned by two parameters, which are hyperelasticity and viscoelasticity.Hyperelasticity can be derived by ftting data obtained from uniaxial tensile tests, while viscoelastic parameters can be obtained by ftting data obtained from relaxation tests.Teoretically, Mooney-Rivlin is more suitable for strain values of 20% to 150% [26].Te maximum strain amplitude in this study is 150%, which all lies in the above interval, so the hyperelastic parameters can be simulated by Mooney-Rivlin.Te specifc parameters of hyperelasticity are listed in Table 3.As for viscoelasticity, the Prony sequence was used to simulate the time dependence of the rubber material, and the parameters used in this simulation are listed in Table 4.

Interaction and Boundary Conditions. Te right-angle dampers in this study interacted in two places in ABAQUS.
For one thing, in practice, the vulcanization bond between the viscoelastic material and the steel plate has strong integrity, so the viscoelastic layer was connected to the steel plate by tie binding in the simulation.For another thing, in the test, the upper part of the damper was connected to the MTS machine through a steel rod, and then, the displacement was applied.Terefore, a point was coupled in the center of the top surface of the shear steel plate in the simulation in order to apply the displacement condition there.
Te boundary conditions of the damper simulation are the same as those of the test.Tis simulation considered four displacement amplitude working conditions at 1.0 Hz for comparing test results and studies on subsequent stress and energy conversion.As shown in Figure 15, a fully fxed boundary condition was applied at the bottom end of the constrained steel plate.At the coupling point on the top surface of the shear steel plate, the displacement boundary condition was imposed, and a sinusoidal function condition was used with the loading controlled by displacement.16.From the fgure, it can be seen that the maximum damping force of the simulated curves at four displacements of 1.2, 3, 6, and 9 mm difers from the maximum damping force of the test results by 5.8%, 9.9%, 4.2%, and 6.9%, respectively, when compared with the test curves.Te maximum viscous force of the simulated curves at four displacements difers from that of the test results by 10.8%, 5.5%, 9.4%, and 5.1%, respectively, and the hysteresis loop area of the simulated curves at four displacements difers from that of the test results by 10.7%, 11.3%, 13.6%, and 0.64%, respectively.It can be seen that the fnite element simulation has less error compared with the experimental results and can be used for the numerical simulation analysis of right-angle viscoelastic dampers.

Stress Analysis of Right-Angle Dampers.
Figure 17 shows the stress distribution between the restraining steel plates and the viscoelastic layers for the maximum deformation of the viscoelastic layers at 1.2, 3, 6, and 9 mm displacement amplitudes.As can be seen from the fgure, the stress on the steel plates is much larger than that on the viscoelastic layers.Te stress distribution on the steel plates is approximately the same when the viscoelastic layers reach the maximum deformation at diferent displacement amplitudes, with the maximum stress at the corner point of the fxed end and radiating from the corner point of the fxed end (see the position of the circles in Figure 17

Analysis of Energy Dissipation of Right-Angle Dampers.
Figure 18 shows the energy dissipation curves of the dampers for displacement amplitudes of 1.2, 3, 6, and 9 mm, and the time of work done by the external forces is all three seconds.Te curves contain external work done (ALLWK), creep dissipation (ALLCD), strain energy (ALLSE), and plastic dissipation (ALLPD).As shown in Figure 18(a), the work done by the external force at a displacement amplitude of 1.0 Hz frequency and a maximum displacement of 1.2 mm for the shear steel plate, i.e., the energy subjected to the damper, is 18.005 N-m, of which the energy dissipated by the viscoelastic material is 17.732 N-m, while the energy dissipated by the plasticity of the whole model is 0 N-m.It can be seen that the damper steel plate was not plastically deformed, and all the energy was basically dissipated by the viscoelastic material.As shown in Figure 18(b), the peak shear deformation of the   Figures 18(c) and 18(d) show the damper energy variation curves for the 6 mm and 9 mm displacement amplitude operating conditions at 1.0 Hz frequency, respectively.From the fgure, it can be seen that the work done by the external force at two displacement amplitudes is 275.129 and 298.315N-m respectively, and the plastic energy dissipation remains 0 N-m.Te viscoelastic energy dissipation is 300.272 and 361.672N-m for the two conditions, and the creep energy dissipation is higher than the work done by the external force.And at this time, the strain energy gradually becomes negative with the increase of external work time, and the energy is −25.197 and −63.598N-m, respectively.At this point, the sum of the viscoelastic material energy dissipation and the negative strain is approximately equal to the work done by the external force.Tis may occur because the strain energy of the viscoelastic material was converted into heat energy and dissipated during the reciprocal shear motion, resulting in a negative situation.Te work done by the external force is a fxed amount.In the simulation analysis of the damper as a whole, in order to maintain the energy conservation law of the object of study   Structural Control and Health Monitoring (ALLWK � ALLCD + ALLSE + ALLPD), the energy consumption of creep will appear to exceed the work done by an external force.Te summary of energy dissipation in the numerical simulation is listed in Table 5, where U max is the displacement amplitude.From Table 5, it can be seen that plastic energy dissipation did not occur throughout the loading at each displacement of the damper, implying that the steel plate of the right-angle damper did not participate in the energy dissipation.Te plastic strain cloud of the damper at 9 mm displacement amplitude in Figure 19 shows that no plastic strain deformation occurred in all parts of the steel plate under the maximum stress loading condition, which again confrms the conclusion that there was no plastic energy dissipation in the damper.It can be seen that the dampers work well, but whether plastic dissipation occurs under large displacement loading conditions, or when largesize steel plates are used, needs to be studied further.

Control Performance Study of RVD
6.1.Overview of Steel Frame Model.In order to verify the damping efect of RVD on the steel frame, the structural response analysis of a single-span four-story scaled-down steel frame structure without control and with control (set up RVD damping system) was carried out in this paper by the method of establishing a refned three-dimensional model in ABAQUS, respectively.Te material used for the steel frame is Q345 steel with a damping ratio of 0.05.Te height and span of the frame are 1 m and 1.5 m, respectively.Te frame beam is the I-beam section with a size of 100 mm × 68 mm × 4.5 mm × 7.6 mm, and the frame column is the box section with a size of 100 mm × 100 mm × 10 mm, as shown in Figure 20.Te efect of placing 1660 kg and 700 kg mass blocks on foors 1 to 3 and foor 4, respectively, was achieved by increasing the density of frame beams.Te dampers of the controlled structure were arranged at the top joints of the beams and columns in the Z-direction of the frame structure (as shown in Figure 21(a)).Figure 21(b) shows the numerical simulation model in ABAQUS.Te size of the polyurethane material layer was 200 mm × 200 mm × 6 mm (length × width × thickness).Te dimensions of the shear and restrained steel plates of RVD were set as 250 mm × 200 mm × 16 mm (length × width × thickness) and 250 mm × 200 mm × 12 mm (length × width × thickness), respectively.Te loading seismic wave was selected as the EI Centro wave.Te duration of the seismic wave was 30 s, and three kinds of peak accelerations (0.1 g, 0.2 g, and 0.4 g) were set for both uncontrolled and controlled structures.

Response of Structural Interstory Displacement.
Comparative graphs of the interstory displacement response of the uncontrolled and controlled structures for the frst foor under three diferent peak accelerations (0.1 g, 0.2 g, and 0.4 g) are given in Figures 22(a)-22(c).From Figure 22, it can be seen that the overall interstory displacement of the controlled frame is smaller than that of the uncontrolled frame during the whole seismic process, indicating that the PUE-type RVD can efectively reduce the interstory displacement of the frame structure during the entire seismic action.
Figure 23 gives the comparison of the maximum interstory displacement distribution curves along the height for each layer of the uncontrolled and controlled structures.Table 6 summarizes the maximum interstory displacement values of the uncontrolled and controlled frames and their damping rates, where the damping rate is the ratio of the diference between the maximum interstory displacement of the uncontrolled structure and the interstory displacement of the controlled structure to the maximum interstory displacement of the uncontrolled structure.As can be seen from Table 6, the damping efect of the maximum interstory displacement of the frame is obvious under diferent peak accelerations, and the damping rates of the displacement are roughly equivalent.Under the three peak accelerations, the damping rate is in the range of 42% to 43% for the frst foor, about 45% for the second foor, and about 47% and 51% for the third and fourth foors, respectively.As the height increases, the damping efect also improves, and the fourth layer has the best damping efect.Under all working conditions, the maximum interstory displacement angle of the uncontrolled structure can reach 0.007 rad, which exceeds the code (0.004 rad).After setting the PUE-type RVD, the maximum interstory displacement angle is reduced to 0.0038 rad, which meets the code.

6.2.2.
Response of Structural Acceleration.Figures 24(a)-24(c) show the comparison of the top-foor acceleration response between uncontrolled and controlled structures at three peak accelerations (0.1 g, 0.2 g, and 0.4 g), respectively.From the fgure, the addition of RVD has a better efect on the acceleration control of the frame throughout the seismic process, while the maximum acceleration of the uncontrolled frame is reduced, indicating that the PUE-type RVD plays a positive role in limiting the acceleration of the frame.
Figure 25 gives the comparison of the maximum acceleration distribution curves along the height for each layer of the uncontrolled and controlled structures.Table 7 summarizes the maximum acceleration values of the uncontrolled and controlled frames and their damping rates, where the damping rate is the ratio of the diference between the maximum acceleration of the uncontrolled structure and the maximum acceleration of the controlled structure to the maximum acceleration of the uncontrolled structure.Combining the graph and table, it can be seen that the maximum acceleration value increases gradually as the number of layers increases, and the maximum value appears at the top layer for both uncontrolled and controlled structures.Te range of damping rates from the frst to the fourth layer under three earthquakes with diferent intensities is 3% to 11%, 29% to 33%, 24% to 26%, and 26% to 30%, respectively, and the second layer has the best efect for acceleration control under the overall comparison.Combining the acceleration response and displacement response, the PUE-type RVD has better control for displacement.
Structural Control and Health Monitoring

Response of Structural Interstory Shear Force.
According to the acceleration time-history response curve obtained by the research model and combined with the mass distribution of the foor of the frame structure, the interstory shear force can be obtained through the following equation: where V i (t) is the shear force of the ith layer, m j is the mass of the jth foor, and a j (t) is the relative acceleration of the jth layer.Figure 26 gives the comparison of the maximum interstory shear force curves along the height for each layer of the uncontrolled and controlled structures.Table 8 summarizes the maximum interstory shear force values of the uncontrolled and controlled frames and their damping rates, where the damping rate is calculated in the same way as the displacement and acceleration.From the fgure and table, it can be seen that the PUE-type RVD has a better control efect on the interstory shear force under all working conditions, and the damping rate reaches more than 30% under all working conditions.Te interstory shear force decreases with the increase of height under the same working condition, and the maximum value appears at the frst layer.Combining all the working conditions, it can be seen that RVD has the best control efect on the interstory shear force for the frst and second layers compared with the other two layers.Structural Control and Health Monitoring

Conclusions
Tis paper studied the dynamic thermodynamic properties of polyurethane damping materials and fabricated rightangle viscoelastic dampers using polyurethane as the energydissipating core material.Ten, the dynamic characteristics of the damper were studied through the self-designed test loading device and scheme.Furthermore, the damper stress analysis and energy dissipation analysis were performed using fnite element simulation.Finally, seismic time-history analysis was performed for uncontrolled and controlled (equipped with RVDs) steel frame structures.Te designed dampers have good energy dissipation capacity and are suitable for seismic resistance of steel frame structures.Te specifc conclusions are as follows: (1) Te TA values of the polyurethane material and the loss factor of the polyurethane right-angle damper both peak at 2.0 Hz, which to a certain extent confrm the accuracy with each other.It is also shown that the polyurethane viscoelastic dampers made in this paper can give good play to the damping properties of viscoelastic damping materials.(2) Te right-angle damper has smooth and full hysteresis curves, with good energy dissipation capacity, and can be used for seismic resistance of assembled steel joints.Te shape of the hysteresis loop varies with the displacement amplitude, and its hysteresis characteristics are of a nonlinear type.At all frequencies, the stifness of the damper decreases with the increase of the displacement amplitude.(3) Te maximum damping force shows a trend of increasing and then decreasing with the increase of displacement amplitude, and the equivalent damping coefcient, storage modulus, loss modulus, and loss factor show a decreasing trend with the increase of the displacement amplitude.Te equivalent damping coefcient at each displacement of the damper gradually decreases with the increase of frequency, while the frequency dependence of other dynamic parameters indexes is not obvious.(4) Te stress distribution of the viscoelastic material layer is basically symmetrical, and the extreme value of the stress appears on the connection line with the steel plate, and the steel plate for constraint appeared at the upper and lower end points of the fxed end.
When the excitation level did not exceed 9 mm displacement amplitude, the energy was dissipated by the polyurethane at diferent excitation levels without plastic deformation of the steel plate.Under the maximum stress loading condition, the right-angle viscoelastic dampers never produced the plastic loss.( 5) Te polyurethane right-angle damper has a good shock absorption efect under diferent earthquake actions.It has played a good role in limiting interstory displacement and acceleration and reducing interstory shear.Te seismic-reduction rate of interstory displacement, acceleration, and interstory shear can reach 51%, 32%, and 36%, respectively.Te results fully prove that polyurethane right-angle damper has signifcant energy dissipation capacity in steel structure joints.

Figure 1 :
Figure 1: Layout of the right-angle viscoelastic damper (yellow part) at beam-column joints.

Figure 4 :
Figure 4: Experimental diagram: (a) geometric dimension of RVD (unit : mm); (b) three-dimensional view of loading device; (c) actual RVD; (d) view of the actual loading device.

4. 4 .
Equivalent Damping Coefcient C d .Te equivalent damping coefcient is a parameter that refects the value of the basic mechanical properties of the damper.As shown in the displacement dependence diagrams of the equivalent damping coefcient in Figure10(a), the four curves show an overall monotonically decreasing trend with the increase of displacement, which is consistent with the variation law of the loss factor derived from the temperature scanning test of energy-consuming materials polyurethane.With the increase in frequency, the curves decrease slowly, and the maximum value of C d is 3.0 N s/mm at the displacement amplitude of 1.2 mm and the loading frequency of 0.5 Hz.Comparing Figures10(a) and 10(b), it can be seen that the displacement dependence and frequency dependence have similar trends.Te equivalent damping coefcient at each displacement shows a monotonically decreasing trend with the increase of frequency, and the decreasing trend becomes slower with increasing displacement amplitude, and the value of C d at the same frequency also decreases gradually.
(a)) to the far side.Te lateral stress in the viscoelastic material layers is essentially equal, and there are areas of increased stress in the middle part of the material layers.On the top surface of the material layers, the stress increases in a parallel linear pattern from the part bonded to the restraining steel plate to the part bonded to the shear steel plate, the latter being the most stressed part of the entire viscoelastic layers.Comparing Figures17(a)-17(d), it can be seen that with the increase of the displacement amplitude, the stress on the steel plates and viscoelastic layers gradually increases.Te maximum stress on the steel plates and viscoelastic layers appears at 9 mm displacement amplitude, and the values are 56.3 and 2.2 MPa, respectively.

Figure 19 :Figure 20 :Figure 22 Figure 21 :
Figure 19: Plastic strain of RVD at the displacement of 9 mm.

Figure 23 :
Figure 23: Curves of maximum interstory displacement along the height distribution for each layer of uncontrolled and controlled frames.

Figure 25 :
Figure 25: Curves of maximum acceleration along the height distribution for each layer of uncontrolled and controlled frames.

Figure 26 :
Figure 26: Curves of maximum interstory shear force along the height distribution for each layer of uncontrolled and controlled frames.

Table 1 :
Test schemes of the viscoelastic damper.

Table 2 :
Plastic parameters of steel.

Table 4 :
Viscoelastic parameters of rubber.
5.4.1.Validation of Finite Element Simulation.A comparison of the fnite element simulated hysteresis curves and the experimental hysteresis curves of the damper at 1.0 Hz frequency and displacement amplitudes of 1.2, 3, 6, and 9 mm is given in Figure

Table 5 :
Summary of energy dissipations obtained from numerical results.

Table 6 :
Comparison of maximum interstory displacement for each layer between the frame without control and the frame with control.

Table 7 :
Comparison of maximum acceleration for each layer between the frame without control and the frame with control.

Table 8 :
Comparison of maximum interstory shear force for each layer between the frame without control and the frame with control.