Investigation of dynamic behavior and seismic performance of cam-type response-amplification friction damper

Test model design

Shaking table test always employs scale-down models since the prototype structure is too huge. In this study, the primary purpose is to investigate the dynamic behavior and real-world effect of the CRAFD device. Therefore, a test on the full-scale CRAFD device, installed on a full-scale model, is preferred rather than a scaled one. A single-layer steel frame structure was selected as the primary test model, as its simplicity allows the test objectives to remain focused on the behavior of the CRAFD device. In addition, the test model was made of steel to exclude the potential nonlinearity in the primary structure. Besides, the fundamental frequency of the test model was set at 3.0 Hz, which was close to the natural frequency of three to four layers buildings. To avoid a too large mass on the shaking table, the steel frame had a total weight of 7023 kg, and the horizontal stiffness at 2.309 kN/mm accordingly. Following the designed properties, the steel frame had 4 I-columns with I-beams at the top, as shown in Figure 1.OPEN IN VIEWER

There was a V-shape diagonal support installed at the top of the frame to provide connection between the ground and the frame. In the uncontrolled steel frame, the V-shape support was separated from the ground. Besides, this test included a bolt-slotted friction damper (FD) and the CRAFD device, which connected the terminal of the V-shape support and the ground. The CRAFD, as shown in Figure 1, consisted of a cam-type response amplification (CRA) device and a lateral FD. The CRA device comprised a ball screw, ball nut, eccentric cam, rectangular frame, horizontal slide rail, and steel plate support. The eccentric cam had a mass of 1.8 kg, and the lateral FD has a design friction force of 1.2 kN. In contrast, the bolt-slotted FD, as the counterpart of the CRAFD, has a design friction force of 12 kN as the CRAFD could significantly amplify the friction force. Figure 2 shows the picture of the single-layer steel frame model and the CRAFD device used in this test.OPEN IN VIEWER

Sensors arrangement and test scenarios

The acceleration, displacement, force and strain responses were measured during the test. Figure 3 shows the configuration of the sensors. There were an accelerator and a displacement meter at both the top and bottom of the test model, as well as at the terminal of the V-shape support. In addition, a force sensor was installed in series with the dampers to measure the axial force in the dampers. A total of 12 strain gauges were installed on the columns and beams of the frame structure to measure the bending moment responses. Particularly, the strain gauges were installed on the V-shape support to identify the potential bending moment on the diagonal components.OPEN IN VIEWER

As the characteristics of different seismic records vary significantly, eight natural seismic records, recommended by the American seismic code ATC-63 in report FEMA-695, were included in this test, and Table 1 lists the information of the selected records. An artificial record (AW) was added as the seismic code also recommend to include an artificial one apart from natural records. Figure 4 shows the accordingly response spectrum of all the records under 1 m/s² with damping ratio of 0.05. The durations of each seismic record are 30.01s (Northridge), 55.89s (Duzce), 29.98s (Coyote Lake), 75.57s (Imperial Valley), 79.98s (Christchurch), 59.99s (Parkfield), 40.95s (Kobe), 79.96s (Loma Prieta), and 43.98s (Artificial wave). Among them, the records from Parkfield, Imperial Valley, and Loma Prieta exhibit pulse-like components, while the other seismic records do not. During the test, the steel frame was excited by the 9 records according to the order in Table 1, under the PGA of 0.2, 0.3 and 0.4 g. To avoid potential damage to the model, the model with CRAFD was tested first, then the model with FD, and finally the uncontrolled model. Each time before the test of the model under certain PGA, the model was subject to a 0.05 g white noise input to detect the natural frequency change of the model.

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Table 1.

Seismic wave information table.

​	Seismic waves	Stations	Magnitude	PGD(cm)
Far-field	Northridge	Beverly-Hills-Mulhol	6.69	7.79
	Duzce	Bolu	7.14	5.84
Near-field	Coyote Lake	Gilroy array #6	5.74	2.76
	Imperial Valley	El Centro array #4	6.53	3.05
	Christchurch	Pages road pumping station	6.2	2.18
	Parkfield	Parkfield - Cholame 3E	6.0	0.7
	Kobe	Nishi-Akashi	6.9	2.17
	Loma Prieta	Corralitos	6.93	4.8
Artificial wave (AW)	/	/	/	7.4

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Figure 4.

Acceleration response spectra of seismic records (PGA = 1 m/s², damping ratio 5%).

Frequency reduction effect

To investigate the dynamic behaviors of the CRAFD, the natural frequency of the frame model was identified under both uncontrolled and controlled conditions. Figure 5 compares the Fourier Spectrum of the acceleration response at A1 of the original, FD and CRAFD model before and after the seismic inputs. The acceleration response seems to has little change after the seismic inputs, as the steel frame and the dampers have little damage. The original, FD and CRAFD model have the natural frequency of 2.9, 4.0 and 5.5 Hz, respectively, and the damped model even has higher natural frequency than the uncontrolled model. As the white noise input only has a PGA of 0.05 g, the FD should not slide and keeps at the sticked status. Therefore, the supplementary stiffness provided by the FD increases the natural frequency of the model under the small white noise input. The supplementary stiffness of the damper in static is beneficial for the structure, helping to protect the structure under wind and service loads. As a comparison, the CRAFD increases the natural frequency more significantly than the FD. The higher static stiffness of the CRAFD arises from the ball-screw pair, which amplifies both the friction force and the axial stiffness. Therefore, from the point of view of normal service condition, the CRAFD shows the advantage over the conventional FD due to the high static stiffness.OPEN IN VIEWER

When the frame is subject to seismic loads, the dampers started to show nonlinearity, and the detected frequency decreases accordingly. Figure 6 shows the identified natural frequencies of the uncontrolled and damped model under various seismic records with PGA = 0.2 g, 0.3 g, and 0.4 g. Under small PGAs, the model with FD and CRAFD both have larger natural frequency than the uncontrolled model. Meanwhile, when the PGA increases, the FD and CRAFD starts to work and the equivalent frequency decreases. Particularly, the CRAFD under 0.4 g seismic inputs always has the lowest equivalent frequency, showing the effect of the negative stiffness resulting from the amplified inertial mass. CRAFD consists of a Cam-type Response -Amplification device (CRA) and a Lateral Friction Damper (Lateral FD). The most important component in CRA is the cam-type inerter, which inherently possesses a dynamic negative stiffness mechanical effect. Therefore, CRAFD can achieve a negative stiffness effect. Under the Northridge record, as an instance, the natural frequency of the uncontrolled model keeps around 2.9 Hz although the PGA varies. Meanwhile, the equivalent natural frequency of the FD model reaches 4.10 Hz when PGA is 0.2 g, and decreases sharply to around 3.1 Hz when PGA is over 0.3 g. Although the frequency of the FD model decreases, it is still larger than that of the uncontrolled model.OPEN IN VIEWER

When the CRAFD model is subject to small white noise input, its identified frequency is higher than the FD model. Meanwhile, when a seismic record with PGA of 0.2 g is used, the identified frequency of the CRAFD is only 3.2 Hz, already smaller than the FD model. The significant decreased frequency shows that although the CRAFD has a larger initial stiffness, it is easier to start to work under seismic inputs than the FD. The magnitude of friction force provided by FD is positively correlated with the preload force of the damper, and the greater the preload force, the more difficult it is for the FD to maintain a sliding state. The design friction force of the traditional FD in this test is 12 kN, while the design friction force of the lateral FD in CRAFD is 1.2 kN. Therefore, CRAFD is easier to maintain a sliding state compared to traditional FD. In addition, as the PGA increases to 0.4 g, the equivalent frequency decreases to 1.91 Hz, even smaller than that of the uncontrolled model. The test results confirm the frequency reduction effect of the CRAFD under seismic inputs, even the device is subject to high-speed motions.

Friction amplification effect

Apart from the supplementary mass resulting from the inter part of the CRAFD, the amplified friction force is another key feature of the device. The total reaction force of the CRAFD, which consists of both friction and inerter components, was measured using force sensors. The inerter force can be estimated using the mass and relative acceleration between the V-shape support and the ground. Therefore, the friction part of the CRAFD is the difference between the measured force and the inerter force. Figure 7(a) compares the friction force time history of CRAFD and the lateral FD under the Northridge record. The design friction force of the lateral FD is 1.2 kN, while the friction force provided by the CRAFD reaches 8 kN, several times larger than that of the lateral FD. The lateral FD only occasionally reaches the sliding force as the seismic input is only 0.2 g. As shown in Figure 7(b), when the PGA increases to 0.4 g, under which the FD slides frequently, and the CRAFD still shows significant amplified friction force. More importantly, the maximum amplified friction force of the CRAFD stays around 8 kN under various PGAs, which can prevent too large friction force in the device.OPEN IN VIEWER

As the CRAFD generates friction and inertial forces, Figure 8 compares the time history curves of the friction and inertial forces. Under the 0.2 g Northridge record, the inertial force provided by the CRA device is slightly higher than the friction force. Under the 0.4 g Northridge record, the inertial force of the CRA device generates up to 15 kN forces under seismic inputs. As a result, the CRAFD is able to generate significant negative stiffness, while the friction force stays around 8 kN. The force time history conforms the reliability of the ball-screw pair in the CRAFD under severe earthquake events, as the device and reduces the natural frequency of the damped structure, which is consistent with the results in Figure 6.OPEN IN VIEWER

The inertial force of the steel frame under seismic inputs is shared by the four columns and the supplementary damper. As shown in Figure 9, due to the huge amplified friction force of the CRAFD, the damper shares around half of the inertial shear force, and significantly reduces the bending moment at the columns. As a comparison, the FD only generates much smaller friction force than the CRAFD, the shear force on the columns is much larger.OPEN IN VIEWER

The near fault seismic input generally has a pulse-like component, challenging the reliability of the inerter-based dampers. In this test, several near-fault record, like the Imperial Valley and Loma Prieta records, have pulse-like components. As shown in Figure 10, the force response and the seismic input shows that the CRAFD reaches the maximum force at the pulse, and the device can sustain the performance even under the near-fault earthquakes.OPEN IN VIEWER

In summary, during the test, the CRAFD shows both the amplification of friction force and frequency reduction due to the inerter effect under the seismic inputs, which are predicted by the theoretical study. More importantly, the device performed reliably under high-velocity motion, validating its ability in seismic events.

Seismic protection principle of the CRAFD based on test data

The CRAFD shows reliability under high speed motions, while its effect on reducing seismic responses is another concern. During the seismic test, the three models, including the original, FD and CRAFD model, are subject to the nine seismic records with various PGAs ranging from 0.2 g to 0.4 g.

Figure 11 compares the peak displacement at the top of the model under all seismic records, as the inter-story drift is the key seismic response for buildings. Under all the seismic inputs, the FD can slightly reduce the peak displacement response, while the CRAFD can further reduce the response by a larger margin. Under PGA = 0.2 g, 0.3 g and 0.4 g, CRAFD reduced the peak displacement by an average of 60.51%, 62.74% and 66.18% respectively, significantly outperforming the FD’s 37.26%, 41.71% and 41.07% reduction respectively. The CRAFD shows significant advantages on reducing the displacement response compared with the FD.OPEN IN VIEWER

Figure 12 shows the time history curve and the corresponding frequency response function (FRF) of displacement response under the Northridge record with a PGA of 0.4 g. According to the time history curves, the FD and CRAFD both can significantly reduce the displacement response. Meanwhile, the FD model introduces notable high-frequency components, attributed to the frequent stick–slip behavior of the FD under seismic excitation. More importantly, the model with the CRAFD generates more low frequency responses around 2 Hz, compared with the FD, showing the frequency reduction effect of the CRAFD.OPEN IN VIEWER

Generally, the displacement of a structure with low frequency is prone to generate large displacement response, the CRAFD shows the contrast results. Since the displacement response is usually governed by a single modal, the displacement time history can be fitted using a single-degree-of-freedom system with specified natural frequency and damping ratio. Figure 13 shows the fitted damping ratios of the original, FD and CRAFD models under various seismic inputs. The uncontrolled model is made of steel with welded connection, so it has a low damping ratio when no damper is installed. After the FD and CRAFD are installed, the damping ratio significantly increases as the dampers provide supplementary energy dissipation. Particularly, the damping ratios under 0.2 g seismic inputs are relatively small, only around 10% for both the two kinds of dampers. Meanwhile, when PGA increases to 0.4 g, the damping ratio sharply increases as the dampers slide frequently. Notably, under all seismic inputs, the CRAFD results in larger damping ratios than the FD, and that’s why the CRAFD achieve better effectiveness on reducing the displacement response.OPEN IN VIEWER

Effect of the CRAFD on reducing seismic responses: Spectral and energy view

The acceleration response relates to the inertial force on the structure, so reducing the acceleration response is the primary way to reduce the seismic responses. As shown in Figure 14, the uncontrolled model generates significant acceleration response, due to the small damping ratio. When the FD is installed, FD reduced the peak acceleration by an average of 5.12%, 9.89% and 15.78% respectively under PGA = 0.2 g, 0.3 g and 0.4 g. Meanwhile, the CRAFD can further reduce the acceleration response, reaching a mitigation rate at 9.51%, 15.67% and 23.25% in average respectively under 0.2 g, 0.3 g and 0.4 g inputs. When the PGA is small, the reduction ratio is small as the FD and CRAFD are hard to slide. Particularly, under all the seismic records, the CRAFD shows better performance than the FD. Besides, when the acceleration response is larger, the CRAFD shows larger mitigation rate, as the sliding in the device prevent high acceleration response.OPEN IN VIEWER

Sliding of friction dampers is the key point in reducing the peak acceleration response. As shown in Figure 15(a), at the beginning of the seismic event, the FD model generates larger acceleration than the uncontrolled one, indicating the FD in the stuck status increases the frequency and the acceleration response. Meanwhile, the CRAFD model, due to the negative stiffness resulting from the inerter, generates smaller acceleration than the FD model. When the CRAFD starts to work, it decreases the frequency and increases the damping ratio. As shown in Figure 15(b), compared with the uncontrolled model, the FD model although significantly reduces the response near 3 Hz, amplifies the response in higher frequency range, as the stuck status increases the stiffness. Meanwhile, the CRAFD reduces the high frequency and 3 Hz components at the same time, and the low frequency components governs the response. Therefore, the CRAFD has its distinctive advantages on reducing the acceleration response.OPEN IN VIEWER

To further investigate the influence of the CRAFD on the primary structure, the wavelet spectra of acceleration response at A3 point are plotted. As shown in Figure 16(a) and (b), although the seismic input primarily compromises 1–2 Hz components, the uncontrolled model generates significant 1–5 Hz acceleration responses. In the FD model, as shown in Figure 16(c), although the spectrum density decreases, the model generates high frequency components around 5 Hz. Particularly, after the seismic input ends, the FD model still generates 5 Hz responses during the attenuation segment. As a comparison, as shown in Figure 16(d), the CRAFD model not only achieves a substantial reduction in spectral density but also confines the response to a lower frequency range of 1–3 Hz. Furthermore, following the end of seismic excitation, the acceleration responses of the CRAFD model attenuate rapidly. Once the CRAFD enters its working state, it simultaneously reduces the structural frequency—thereby lowering the acceleration response—and increases the damping ratio, which accelerates response decay. These observations are consistent with the findings presented in Figure 15.OPEN IN VIEWER

Figure 17 shows the energy time history of the three structures under 0.4 g Northridge record, and Tables 2–4 show the proportion of input energy for each part under 0.4 g various records. E_i is the seismic input energy, E_k and E_y are the kinetic and strain energy of the structure, respectively. E_d, E_s, E_s-friction force and E_s-inertial force represent the energy dissipation of the structure, traditional FD, CRAFD friction force and inertial force, respectively. When there is no supplementary dampers to dissipate the seismic energy, the input energy is absorbed by the primary structure itself. Although the traditional FD is installed, the strain energy of the structure E_y still accounts for the highest proportion, the damping energy dissipation by the damper E_s is even lower than that of the structure E_d. The curve of E_s seldom fluctuates, as the traditional FD is easy to stick when the external force is not large enough. As a comparison, the negative stiffness and frequency reduction effect of CRAFD improve the energy dissipation ratio, and reduce the overall dynamic response of the structure accordingly. Although the inertia force of CRAFD is large, its main role is to provide negative stiffness effect, and the energy dissipation effect is relatively small. At the same time, due to the friction amplification effect of CRAFD, the total friction energy dissipation of CRAFD is much higher than the structural strain energy, which is the primary form of energy dissipation. Therefore, it can significantly reduce the dynamic response of the structure, thereby protecting the structure from damage or destruction caused by ground motion.OPEN IN VIEWER

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Table 2.

Energy components of uncontrolled structure.

​	Total input energy (kJ)	Energy components
	Ei	Ek (%)	Ey (%)	Ed (%)
Northridge	95.63	4.97	68.89	26.14
Duzce	102.75	11.55	64.12	24.33
Artificial wave	105.34	13.72	62.54	23.73
Coyote Lake	103.39	12.10	63.72	24.18
Imperial Valley	100.16	9.26	65.78	24.96
Christchurch	75.57	8.80	58.12	33.08
Parkfield-02	98.87	8.08	66.64	25.29
Kobe	97.36	6.65	67.67	25.68
Loma Prieta	99.73	8.87	66.06	25.07

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Table 3.

Energy components of FD structure.

​	Total input energy (kJ)	Energy components
	Ei	Ek (%)	Ey (%)	Ed (%)	Es (%)
Northridge	95.63	2.41	49.88	26.59	21.13
Duzce	102.75	9.17	46.42	24.75	19.66
Artificial wave	105.34	11.40	45.28	24.14	19.18
Coyote Lake	103.39	9.74	46.13	24.59	19.54
Imperial Valley	100.16	6.82	47.62	25.39	20.17
Christchurch	75.57	5.51	48.55	26.33	19.61
Parkfield-02	98.87	5.60	48.24	25.72	20.44
Kobe	97.36	4.14	48.99	26.12	20.75
Loma Prieta	99.73	6.42	47.83	25.50	20.26

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Table 4.

Energy components of CRAFD structure.

​	Total input energy (kJ)	Energy components
	Ei	Ek (%)	Ey (%)	Ed (%)	Ed-friction force (%)	Ed-inertial force (%)
Northridge	95.63	0.76	24.87	18.99	44.34	11.04
Duzce	102.75	1.27	23.14	17.67	47.64	10.28
Artificial wave	105.34	1.32	22.58	17.24	48.84	10.03
Coyote Lake	103.39	1.29	23.00	17.56	47.94	10.21
Imperial Valley	100.16	1.15	23.74	18.13	46.44	10.54
Christchurch	75.57	1.52	25.17	18.02	45.04	10.25
Parkfield-02	98.87	1.06	24.05	18.37	45.84	10.68
Kobe	97.36	0.94	24.43	18.65	45.14	10.85
Loma Prieta	99.73	1.12	23.84	18.21	46.24	10.59

Seismic protection of the primary structure by the CRAFD

Figure 18 shows the strain time history curve of the column root section (S9) under 0.4 g Coyote Lake record, and Figure 19 compares the peak strain under Coyote Lake with various PGAs. When the FD is installed, the structure still generates significant high frequency responses around 3 Hz shown in Figure 18(b), which results in large strain response as shown in Figure 18(a). As the PGA reaches 0.4 g, the FD remains in a slipping state more frequently than in a stuck state, as evidenced by the reduced 4 Hz components in Figure 18(b). In contrast, the CRAFD further reduces the strain response, particularly in the frequency range near the natural frequency of the primary structure (around 3 Hz). The CRAFD not only mitigates acceleration and displacement responses but also substantially reduces strain responses, thereby providing enhanced protection to the primary structure. In addition, the CRAFD makes the root mean square (RMS) of the strain response smaller than that under FD, which also helps to prevent structure damage under seismic events.OPEN IN VIEWER

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Figure 19.

Peak strain of structural column base under Coyote Lake.

As shown in Figure 19, the peak strain response of the uncontrolled structure and the FD damped increases approximately linearly with the PGA under the Coyote Lake record. The FD demonstrates a consistent and stable mitigation effect on the structural response. In comparison, the CRAFD achieves a further reduction in strain response relative to the FD, and more importantly, exhibits greater effectiveness under stronger ground motions. Particularly, the structure with CRAFD generates similar peak strain response under 0.3 and 0.4 g, showing the CRAFD is more effective under extreme seismic events.

Although the test model is symmetric in geometry, the supplementary FD and CRAFD may introduces out-of-plane deformation of the V-shape link. Figure 20 shows the peak strain at two sides of the two components of the V-shape link under the Coyote Lake record. When the damper is absent, the V-shape link still generates slight bending moments, as the test model has torsional motion under the uniaxial seismic input. When the FD is installed, there is still considerable bending moment at the V-shape link, as the strain responses at the two sides of the components are different. As a comparison, when the CRAFD is installed, the difference between the strain response, which reflects the bending moment response at the V-shape link, is only 4% and is much smaller than that with the FD. CRAFD includes rectangular frame, directional track, and lateral FD, all of which exert out-of-plane constraints on the V-shaped link, so CRAFD can suppress the out-of-plane deformation of the V-shaped link. Therefore, the CRAFD helps to improve the stability of the V-shape link, as the small bending moment helps to increase the allowable compression loads.OPEN IN VIEWER