An experimental approach on energy dissipation of bolted joints using a modified oscillator device

Abstract

A modified and simplified oscillator device is designed and manufactured to investigate the effects of contact roughness and bolt arrangements on energy dissipation caused by joint damping. Three types of surface roughness and five different bolt arrangements are discussed. Identification of Iwan model based on experimental data is carried out. It is indicated that rough surface dissipates more energy than smooth one. Specimens with more bolts dissipate relatively more energy. When bolt number is consistent, the series type dissipates more energy than the parallel type. Experimental data show a good stability and accuracy of the proposed oscillator device. The identified Iwan model provides a good conformity with the reconstructed hysteresis loop. The four-parameter Iwan model can well describe the damping property of joints with different surface roughness and bolt arrangements.

Keywords

Damping oscillator device roughness bolted joint resonant excitation

1. Introduction

Complex structures in engineering practice are commonly assembled by a large number of jointing components. Recent investigations (Ames et al., 2009; Gaul and Schmidt, 2019; Xiao et al., 2014) have shown that micro- and macro-slipping will occur on contact interfaces of jointing components under external loads. These phenomena are responsible for nonlinear contact stiffness and structural damping (Bograd et al., 2011; Gaul and Nitsche, 2001). On the other hand, contact interfaces are also an important source of structural uncertainty (Mignolet et al., 2015). As the contact interfaces are tightened to each other, a direct experimental approach to observe their mechanical processes is often impractical. Therefore, indirect approaches (Ames et al., 2009) using whole joint-level specimens are applied.

Focusing on several types of joints applied in aerospace engineering, Ungar (1973) found that contact slipping caused by external loads is the main reason for joint damping. Hysteresis loop in force–displacement plane was initially applied to calculate dissipated energy of damping by Metherell and Diller (1968). Nonlinear variations of contact stiffness over applied force were also observed. A tangential harmonic oscillator was designed by Gaul and Lenz (1997) to provide sinusoidal excitations with various amplitudes on dumbbell device. The instrument was then deployed to carry out experimental research on jointed structures. Hysteresis loops under different applied loads were obtained. The big mass device (BMD) Ames et al. (2009) designed by Sandia National Laboratory was used in dynamic analysis of three different types of joints including “flat lap,” “stepped lap,” and “curved lap” joints. Power law relationships of energy dissipations versus applied loads were observed, which varied from 2.4 to 3.0. To obtain a precise and reliable description of the transition between micro- and macro-slip, quasi-static experiments of eight different preloads were carried out by Resor and Starr (2008). It showed that tangential contact stiffness during micro-slip stage tended to be linear. Initiation of macro-slip was observed at a length scale of 10⁻⁶ m. Hysteresis loops of aluminum and steel joints under different preloads were obtained by Eriten et al. (2011a, 2011b, 2012) from their quasi-static and dynamic experiments. It is indicated that aluminum joints generally dissipated more energy than steel joints.

Different approaches of constitutive modeling for jointed structures are also carried out (Ahmadian and Rajaei, 2014; Li et al., 2019a, 2019b; Miller and Dane Quinn, 2009; Oldfield et al., 2005; Quinn and Segalman, 2005; Rajaei and Ahmadian, 2014; Segalman and Starr, 2008; Wang et al., 2018). These approaches can be generally concluded as two types: (1) a top-down, phenomenological modeling and (2) a bottom-up, physical-based modeling. Examples of the first approach are Segalman’s (2002) four-parameter Iwan model, Song et al.’s (2004) adjusted Iwan model, and the six-parameter Iwan model (Li and Hao, 2016; Li et al., 2017). In the other type of modeling, rough contact theories at micro- or nanoscale are directly applied to establish the constitutive relationship (Argatov and Butcher, 2011). Based on the rough contact theory and zero thickness element (ZTE), a multi-scale constitutive model for contact interface of jointed structures was developed by Balaji et al. (2020). Considering multi-asperity contact and fractal contact theory, Zhang et al. (2019) proposed a multi-scale model for uneven contact interfaces of joints.

Among those modeling approaches, Iwan-type model is widely applied. Identification of Iwan model depends on precise experimental data of jointed structures. Quasi-static experimental investigations (Ames et al., 2009; Eriten et al., 2012; Resor and Starr, 2008; Xu et al., 2020) indicate a weak nonlinearity of contact stiffness during micro-slip stage, which is relatively difficult to capture. Therefore, measuring joint damping through dynamic experiments is often considered. A systematic experimental research by Ames et al. (2009) shows that the BMD is efficient to capture joint damping. A detailed introduction about energy dissipation caused by frictional contacts is given and different joint types and preloads are specifically discussed.

In this article, the BMD device is modified and simplified to an oscillator to measure energy dissipation caused by joint damping is designed and manufactured. Effects of contact roughness and bolt arrangements on energy dissipation are discussed. A calculation formula of energy dissipation represented by equivalent viscous damping is derived in Section 2. An introduction of the oscillator device and its finite element method (FEM) modal analysis is given in Section 3. Detailed experimental procedures are shown in Section 4. Experimental results under different conditions are provided in Section 5. Identifications of Iwan model based on experimental results are carried out in Section 6. Summary and conclusions of this article are given in Section 7.

2. Energy dissipation of equivalent viscous damping

Initiation of macro-slip was observed at a length scale of 10⁻⁶ m according to quasi-static experiments of jointed structures (Ames et al., 2009; Resor and Starr, 2008). If hysteresis loops of force displacement relationship were obtained directly in a quasi-static way, the data of interest might be swamped by instrumental measurement errors or noises. The Sandia National Laboratory developed a dynamic experimental device (Ames et al., 2009) to study nonlinear damping properties of joints. Experimental data of high precision were obtained. Inspired by their experimental device, an single degree-of-Freedom (SDOF) oscillator as illustrated in Figure 1 is considered and designed in this study. In Figure 1, A_m(t) and A_b(t) represent accelerations of the mass and the base, respectively. An equivalent viscous damping c_eq is considered to represent structural damping caused by contact friction of joint interfaces. Stiffness of the joint is represented by k. For the proposed SDOF system, energy dissipation of the equivalent viscous damping, ΔE, can be calculated as the integral form of a closed trajectory in phase plane, which can be given as

Δ E = \oint c_{e q} \dot{x} d x

(1)

where x represents displacement of the mass. Equation (1) can be rewritten as an integral over time t. Therefore, the energy dissipation over one load period T can be further obtained as

Δ E = \int_{0}^{T} c_{e q} \dot{x} d t = π c_{e q} ω Y_{m}^{2}

(2)

where Y_m is the displacement amplitude of the mass and ω the frequency of excitation.

Figure 1.

Scheme of a base-excited single degree-of-Freedom oscillator.

As for a base-excited SDOF oscillator, the ratio of its motion amplitude to that of the base is called the transmissibility, or TR. It can be written as

T R = T R (ω) = \sqrt{\frac{1 + {(2 ζ ω / ω_{n})}^{2}}{{(1 - ω^{2} / ω_{n}^{2})}^{2} + {(2 ζ ω / ω_{n})}^{2}}}

(3)

where ω_n is the resonant frequency of the SDOF oscillator and ζ the damping ratio. When excitation frequency ω gradually approaches the resonant frequency ω_n and for ζ << 1, the TR can also be called as the quality factor Q

Q = T R (ω_{n}) \approx \frac{1}{2 ζ}

(4)

Therefore, the equivalent viscous damping c_eq can be derived as

c_{e q} = 2 m ζ_{n} = (\frac{m ω_{n}}{Q})

(5)

As the quality factor Q can be measured as Q = A_m/A_b, substitution of equation (5) into (2) yields

Δ E = (\frac{π m A_{m} A_{b}}{ω_{n}^{2}}) = (\frac{m A_{m} A_{b}}{4 π f^{2}})

(6)

All physical quantities in equation (6) can be determined directly from dynamic testing using the proposed SDOF oscillator. The mass of the oscillator, m, can be measured before testing. A_m and A_b can be obtained as the acceleration amplitudes of the mass and the base, respectively. For safety and controllability reasons, the chosen excitation frequency f in this experiment is slightly lower than the determined resonant frequency.

3. Design and FEM analysis

The oscillator device in this article is made of 45# Steel. Its dimensions are shown in Figure 2. A centering slot (30.5 mm in wide and 2 mm in deep) is machined at the bottom of the device to locate joint specimens. A groove (190 mm in deep and 30 mm in diameter) is located along the central axis of the device. When the upper piece of the specimen pair is placed in the centering slot, an M8 bolt is then applied to tighten it with the oscillator using a T-type wrench through the groove. Note that the holes of 6 mm are prepared for later tests with flat lap joints. Their preloads are applied by a pair of rollers and two tensioning cables passing through these holes.

Figure 2.

Dimensions of the oscillator, unit in mm.

Before the oscillator has been manufactured, a simplified finite element model is established in Abaqus to investigate its dynamical properties. As 45# steel is applied, density of the model is considered as 7.85 × 10³ kg/m³. Young’s modulus is set as 210 GPa and Poisson’s ratio is set as 0.33. Contact interfaces between two specimen pairs and the oscillator are neglected. These interfaces are simplified into binding constraints. Bolts, nuts, washers, and other properties with relatively small size are also neglected. The established FEM model as plotted in Figure 3 contains 24,813 brick elements in total.

Figure 3.

Meshing of the finite element Method model.

The first six modes and their corresponding frequencies of the oscillator system are obtained from modal analysis as pictured in Figure 4. Mode 1 (18.8 Hz) and Mode 2 (25.8 Hz) seem to be a pair of orthogonal bending modes. The difference in their natural frequencies is resulted by asymmetries of the single bolt specimen. The first two modes have the ability to excite the interface to bend in xz and zy planes. Unlike the responses of dumbbell device (Ames et al., 2009), a torsional mode is observed at 36 Hz. Generally, a torsional mode of dumbbell device is not easily excited by axial inputs. Tangential deformations are observed in Mode 4 and Mode 5 at the frequency of 242.8 Hz and 251 Hz, respectively. These two modes provide the most valuable response for an x-axis input, which is mainly concerned in this study. Beyond the first five modes, a significantly high frequency of 442.9 Hz is obtained as Mode 6 with a high-order, local deformation at the joint specimen. According to the simplified simulation described above, the driving frequency of interest should be around 240–250 Hz. It is sufficiently far from any other structure modes, which assures that testing of the SDOF oscillator is as straightforward as possible, with little influence by other adjacent modes.

Figure 4.

Mode 1–6 of the oscillator device.

4. Experimental procedures

Joint specimens are made of 45# steel. They are carefully cleaned with compressed air and alcohol before testing. The lower piece of the specimen pair is tightened to a fixture using an M8 bolt. Then, the fixture is tightened on an electrodynamic shaker. When the upper piece of the specimen pair is placed in the centering slot, an M8 bolt is applied to tighten it with the oscillator using a T-type wrench through the machined groove. The oscillator device is then lowered over the specimen attached to the fixture by a crane and rubber wires. Adjustments are performed to make the contact interfaces of the two specimen pieces overlap with each other. When the desired position is achieved, a set of bolt, nut, and washers is applied to tighten the two pieces. A bolt preload of 24 Nm is applied using a digital torque wrench. Three uniaxial acceleration sensors are located at the fixture, the lower, and the upper piece specimen, respectively. They are arranged along the central axis of the shaker to ensure the accuracy of the experiment.

Effects of contact roughness and bolt arrangements on energy dissipation are discussed in this article. Five different arrangements are designed as single bolt, two bolts in series, two bolts in parallel, three bolts in series, and three bolts in parallel. The single bolt specimen is designed with three different contact roughness as smooth, medium, and rough. To verify the repeatability, three identical pairs of specimens are considered for each set. The proposed oscillator device and experiment specimen are shown in Figure 5. Conditions of each set are given in Table 1. A schematic showing both the upper and lower pieces of the specimens are given in Figure 6.

Figure 5.

(a) The oscillator device with single bolt specimens from the front and back view, respectively. (b) Two bolts and three bolts specimens. (c) A sketch of the complete setup. (d) Detailed dimensions of the specimens.

Table 1.

Experiment sets.

Set no	Bolt arrangement	Roughness	Preload (nm)	Pair
1	1 bolt	Smooth	24	3
2	1 bolt	Medium	24	3
3	1 bolt	Rough	24	3
4	2 bolts in series	Rough	24	3
5	2 bolts in parallel	Rough	24	3
6	3 bolts in series	Rough	24	3
7	3 bolts in parallel	Rough	24	3

Figure 6.

The upper and lower pieces of specimens.

For each experiment set, sinusoidal sweeps with different amplitudes (0.1–1.2 g) are performed to determine the corresponding resonant frequencies. According to the simulated modal results in Section 3, the sweep range is considered as 100–1000 Hz. Logarithm sweeping of 1 otc/min is applied. When the resonant frequency is obtained, a fixed-frequency excitation can be performed. It should be noted that for safety and controllability reasons, the chosen excitation frequency is slightly lower than the obtained resonant frequency. When a steady state is achieved, the peak value of each acceleration sensor is recorded.

Taking Set 7 (3 bolts in parallel), for example, the acceleration–time curves of sinusoidal sweep, 0.1 g, is plotted in Figure 7. A_c represents the acceleration of control point on the fixture, A_b the base, and A_m the mass. A pre-sweep is carried out at the first 20 s to check the experimental facilities. If no errors were reported during pre-sweep, a sweep from 100 to 1000 Hz then begins. Readings of the three acceleration sensors hardly change with the increase of loading frequency during the first 90 s. The readings increase sharply after 100 s. A peak point is observed around 110 s. Acceleration amplitude of the control point reaches 6 g. Acceleration amplitude of the base reaches 5.8 g and that of the mass reaches 3.5 g. The resonant frequency is determined as 273 Hz. A duration of 0.02 s was intercepted in two different stages. From 25 s to 25.02 s, readings of the three sensors are nearly the same as the input value, 0.1 g, with obvious high-frequency noises. From 106.93 s to 106.95 s, obvious deviation can be observed. The reading of A_m reaches 1.3 g, which is 13 times of the input value. The curve is smooth and appears to be a linear response. A_b can be characterized as multi-harmonic. These phenomena agree with the observations by Ames et al. (2009).

Figure 7.

Results of sinusoidal sweep of Set 7, 0.1 g.

5. Experimental results

5.1. Influence of surface roughness

Three different kinds of roughness are considered as smooth, medium, and rough. Surfaces of the specimens are scanned with a range of 500 μm along the direction of relative motion using a 3D profilometer, as illustrated in Figure 8. The tested roughness is shown in Table 2.

Figure 8.

Scanned results of roughness.

Table 2.

Scanned results of roughness.

Set no		Surface roughness Ra(μm)
Set no		Upper specimen	Lower specimen
Set 1	Pair 1	0.77	0.82
	Pair 2	0.64	0.89
	Pair 3	0.72	0.91
Set 2	Pair 1	1.23	1.40
	Pair 2	1.10	1.13
	Pair 3	1.28	1.39
Set 3	Pair 1	2.88	2.76
	Pair 2	2.60	2.89
	Pair 3	2.90	2.84

Energy dissipations of joint specimens with different surface roughness are not the same. For Set 1 with smooth surface, the tested roughness ranges from Ra0.64 to Ra0.91. The energy dissipation is relatively large. For Set 2 with medium surface, the tested roughness ranges from Ra1.1 to Ra1.4. Its energy dissipation is slightly lower than that of Set 1. The lowest results are observed in the test with Set 3, Ra2.6 to Ra2.9. These data are illustrated in Figure 9. The abscissa of the figure represents the input force provided by the shaker to the system, which is computed as the mass of the oscillator times its acceleration amplitude A_m under harmonic motion.

Figure 9.

Energy dissipation with different surface roughness.

Slipping of contact interfaces is responsible for energy dissipation. The actual contact area of a jointed structure is related to surface roughness. For rough interfaces, the real contact area is small, thus high local pressure will be found. In this circumstance, local lockup might happen and micro-slipping is prevented. For smooth interfaces under the same preload, the real contact area is relatively larger and the local pressure is also lower than rough interfaces. In this circumstance, micro-slipping could easily occur when subjected to tangential loads. Therefore, smoother interfaces would result in higher dissipation. This interesting phenomenon is also observed by Ames et al. (2009) and Eriten et al. (2011b).

5.2. Influence of bolt arrangement

As listed in Table 1, there are five kinds of bolt arrangements in total. For every set, the preload torque is considered as 24 Nm. These specimens are all manufactured with rough surfaces. Their test roughness ranges from Ra2.35 to Ra3.13. Experiment results are plotted in Figure 10.

Figure 10.

Energy dissipation with different bolt arrangement.

It is clearly shown that specimens with 3 bolts in series dissipate more energy than other types of specimens. For the other four sets (1 bolt, 2 bolts in series, 2 bolts in parallel, and 3 bolts in parallel), with a force smaller than 1250 N, energy dissipations show no significant differences. When the force grows larger than 1750 N, their differences become apparent. These results show that specimens with more bolts dissipate relatively more energy. When bolt number is consistent, the series type dissipates more energy than the parallel type.

5.3. Repeatability of identical specimens

Experiment data of all the three specimen pairs of Set 3 are plotted in Figure 11. Good conformities show that the energy dissipations obtained from the very same experimental process are well repeatable for the identical specimens. It also proves the stability of the proposed oscillator device.

Figure 11.

Comparison of identical specimens with error bars of ±6%, single bolt with rough surfaces.

5.4. Experimental data

It should be noted that with the influence of surface machining accuracy and test controlling errors, obvious wear is created in some of the joints. Influence of wear can be evaluated by the waveform quality of A_c, A_b, and A_m. Regardless of force level, as long as the output waveform of each acceleration sensor is good and stable, the test can be considered as not be affected by wear and can be continued. Wear can also be distinguished by sound. A continued sharp noise from the device during a test is the most obvious sign of wear. When this happens, the test should be terminated immediately to avoid unexpected dangers. For these tests with damaged specimens, steady states cannot be realized during fixed-frequency excitations. The relevant data were rejected and not applied. Experimental data under different conditions are shown in Table 3. The listed data include all results obtained including those presented in Figure 9–11.

Table 3.

Experimental data under different conditions.

Set no	Force (N)	Energy dissipation (J)	Set no	Force (N)	Energy dissipation (J)
Set 1, 1 bolt, smooth	1160	1.69 × 10⁻²	Set 3, 1 bolt, rough	872	2.78 × 10⁻³
	1456	3.11 × 10⁻²		1237	5.43 × 10⁻³
	1654	4.70 × 10⁻²		1538	1.08 × 10⁻²
	1901	7.26 × 10⁻²		1769	1.36 × 10⁻²
Set 2, 1 bolt, medium	1438	2.06 × 10⁻²		2265	2.55 × 10⁻²
	1739	3.56 × 10⁻²		2710	4.10 × 10⁻²
	2032	5.28 × 10⁻²		3025	5.67 × 10⁻²
	2212	6.99 × 10⁻²		3223	7.12 × 10⁻²
Set 4, 2 bolts in series	674	1.63 × 10⁻³	Set 5, 2 bolts in parallel	199	1.79 × 10⁻⁴
	1102	4.80 × 10⁻³		538	1.32 × 10⁻³
	1346	7.90 × 10⁻³		1071	5.49 × 10⁻³
	1537	1.13 × 10⁻²		1736	1.56 × 10⁻²
	1691	1.51 × 10⁻²		2349	3.11 × 10⁻²
	1750	1.78 × 10⁻²		2538	3.95 × 10⁻²
	2019	2.61 × 10⁻²		2866	5.49 × 10⁻²
	2253	3.58 × 10⁻²		3089	6.96 × 10⁻²
	2468	4.69 × 10⁻²		3252	8.42 × 10⁻²
Set 6, 3 bolts in series	183	2.20 × 10⁻⁴	Set 7, 3 bolts in parallel	492	6.24 × 10⁻⁴
	269	6.63 × 10⁻⁴		813	2.23 × 10⁻³
	307	7.82 × 10⁻⁴		992	4.16 × 10⁻³
	377	1.48 × 10⁻³		1189	7.12 × 10⁻³
	511	2.77 × 10⁻³		1334	1.04 × 10⁻²
	704	6.07 × 10⁻³		1456	1.41 × 10⁻²
	945	1.21 × 10⁻²		1788	2.39 × 10⁻²
	1244	1.98 × 10⁻²		2066	3.55 × 10⁻²
	1742	4.07 × 10⁻²		2281	4.79 × 10⁻²

Figure 12.

Comparisons between identified Iwan models and experimental data of (a) different contact roughness and (b) different bolt arrangements.

Figure 13.

Results of Set 3, 1.2 g input: (a) acceleration–time curves and (b) reconstructed hysteresis loop compared with the identified Iwan model.

6. Applications of Iwan model

According to the procedures provided by Li and Hao (2016), the four-parameter Iwan model can be identified with the experimental data from Section 5. Parameter R and χ represent the power law distribution of Iwan model. Parameter φ₂ is the initiation of macro-slip and K₂ is the stiffness variation at the transition between micro- and macro-slip. The analytical expression between dissipation D and displacement amplitude ψ is derived as

D (ψ) = \frac{4 R ψ^{x + 3}}{(χ + 2) (χ + 3)}

(7)

The analytical force–displacement relationship is

F (ψ) = (\frac{R φ_{2}^{χ + 1}}{χ + 1} + K_{2}) ψ - (\frac{R ψ^{χ + 2}}{(χ + 1) (χ + 2)})

(8)

According to equations (7) and (8), the analytical force–dissipation relationship can then be represented as

F (D) = (\frac{R φ_{2}^{χ + 1}}{χ + 1} + K_{2}) {[\frac{D (χ + 1) (χ + 3)}{4 R}]}^{(1 / χ + 3)} - \frac{R}{(χ + 1) (χ + 2)} {[\frac{D (χ + 2) (χ + 3)}{4 R}]}^{((χ + 2) / (χ + 3))}

(9)

With experimental data listed in Section 5 and equation (9), the parameters R、, χ、, φ₂, and K₂ of the Iwan model can be identified in a numerical approach as listed in Table 4. Among those four parameters, R and χ can intuitively reflect energy dissipation characteristics. The identified results show that the energy dissipation grows faster with smaller value of χ, and the energy dissipation will also be larger with larger R. For single bolt specimens, R is larger for smooth interfaces. For two- and three-bolt specimens, R of series types is larger than that of parallel types. Comparisons of the identified Iwan model and experimental data are plotted in Figure 12. Parameter χ varies from −0.7 to −0.05, which also agrees with the observations by Ames et al. (2009) and Eriten et al. (2011a, 2011b). It is shown that the four-parameter Iwan model can well reproduce joint damping properties with different contact roughness and bolt arrangements.

Table 4.

Identification results under different conditions.

Set	Bolt arrangement	Roughness	φ₂ (m)	K₂ (N/m)	R (N/m^{2 + χ})	χ
1	1 bolt	Smooth	7.01 × 10⁻⁴	2.91 × 10⁶	3.16 × 10⁸	−0.05
2	1 bolt	Medium	2.02 × 10⁻³	1.58 × 10⁶	5.54 × 10⁶	−0.27
3	1 bolt	Rough	9.62 × 10⁻⁴	4.63 × 10⁶	4.89 × 10⁶	−0.51
4	2 bolts in series	Rough	1.98 × 10⁻³	2.17 × 10⁶	2.63 × 10⁶	−0.38
5	2 bolts in parallel	Rough	2.99 × 10⁻³	1.78 × 10⁶	2.34 × 10⁶	−0.30
6	3 bolts in series	Rough	2.98 × 10⁻³	2.05 × 10⁶	2.33 × 10⁷	−0.13
7	3 bolts in parallel	Rough	2.74 × 10⁻³	2.25 × 10⁶	4.11 × 10⁵	−0.70

Displacement–time curves of the base and the oscillator can be calculated with the obtained acceleration–time curves. In this manner, the hysteresis loop of force–displacement relationship can be reconstructed. Acceleration curves during the whole fix-frequency excitation of Set 3, 1.2 g, input are shown in Figure 13(a). 24,000 data points from 24.6 s to 29.3 s, as amplitudes are gradually enlarged, are chosen for analysis. A comparison between the identified Iwan model and the reconstructed hysteresis loop are illustrated in Figure 13(b). It can be observed that the color at edge is darker than inside of the loop, which indicates a fixed boundary as the response of the oscillator device tends to be stable. The closed loop of navy blue represents the identified Iwan model. Although the reconstructed hysteresis loop is not in a regular shape, its area is almost the same as that of the identified Iwan model. It proves that the four-parameter Iwan model can well describe the damping property of joints.

7. Conclusions

In this article, a modified and simplified oscillator device is designed, manufactured, and applied to study the energy dissipation caused by joint damping. Compared with the BMD, the oscillator in this study has two advantages. First, mass of the oscillator (101.55 kg) is similar to that of the BMD (205lb, 93 kg), whereas its shape has been redesigned with lower center of gravity. For all those tests with different frequencies, specimens, and input excitations, the stability of the oscillator has been well remained without any support frames. Second, the applied force with the BMD varies from 120 lb to 320 lb (534 N–1424 N). Range of the applied force with the oscillator is 183 N–3252 N, which is much wider than that of the BMD. More testing data can be acquired by the oscillator than the BMD. Experimental data under different conditions show a good stability and accuracy of the proposed oscillator device. It is planned to be deployed in future investigation of jointed structures.

Three different levels of surface roughness and five kinds of bolt arrangements are specifically discussed. The acquired data indicate rough surface dissipates more energy than smooth one. Specimens with more bolts dissipate relatively more energy. When bolt number is consistent, the series type dissipates more energy than the parallel type. Model identifications based on experimental data are carried out. The reconstructed hysteresis loop and the identified Iwan model match well with each other. It is shown that the four-parameter Iwan model can well describe the damping property of joints with different surface roughness and bolt arrangements.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Natural Science Foundation of China under Grant No. 51974171.

ORCID iD

Yikun Li

Appendix 1

References

Ahmadian

Rajaei

(2014) Identification of Iwan distribution density function in frictional contacts. Journal of Sound and Vibration 333(15): 3382–3393.

Ames

Lauffer

Jew

, et al. (2009) Handbook on Dynamics of Jointed structuresSAND2009-4164. Albuquerque, NM: Sandia National Laboratories.

Argatov

Butcher

(2011) On the Iwan models for lap-type bolted joints. International Journal of Non-Linear Mechanics 46(2): 347–356.

Balaji

Chen

Brake

MRW

(2020) Traction-based multi-scale nonlinear dynamic modeling of bolted joints: formulation, application, and trends in micro-scale interface evolution. Mechanical Systems and Signal Processing 139: 106615.

Bograd

Reuss

Schmidt

, et al. (2011) Modeling the dynamics of mechanical joints. Mechanical Systems and Signal Processing 25(8): 2801–2826.

Eriten

Lee

C-H

Polycarpou

(2012) Measurements of tangential stiffness and damping of mechanical joints: direct versus indirect contact resonance methods. Tribology International 50: 35–44.

Eriten

Polycarpou

Bergman

(2011a) Development of a lap joint fretting apparatus. Experimental Mechanics 51(8): 1405–1419.

Eriten

Polycarpou

Bergman

(2011b) Effects of surface roughness and lubrication on the early stages of fretting of mechanical lap joints. Wear 271(11): 2928–2939.

Gaul

Lenz

(1997) Nonlinear dynamics of structures assembled by bolted joints. Acta Mechanica 125(1): 169–181.

10.

Gaul

Nitsche

(2001) The role of friction in mechanical joints. Applied Mechanics Reviews 54(2): 93–106.

11.

Gaul

Schmidt

(2019) Finite element simulation and experiments on rotor damping assembled by disc shrink fits. Mechanical Systems and Signal Processing 127: 412–422.

12.

Botto

, et al. (2019a) A micro-slip friction modeling approach and its application in underplatform damper kinematics. International Journal of Mechanical Sciences 161–162: 105029.

13.

Liu

, et al. (2019b) A modified IWAN model for micro-slip in the context of dampers for turbine blade dynamics. Mechanical Systems and Signal Processing 121: 14–30.

14.

Hao

(2016) A six-parameter Iwan model and its application. Mechanical Systems and Signal Processing 68–69: 354–365.

15.

Hao

Feng

, et al. (2017) Investigation into discretization methods of the six-parameter Iwan model. Mechanical Systems and Signal Processing 85: 98–110.

16.

Metherell

Diller

(1968) Instantaneous energy dissipation rate in a lap joint-uniform clamping pressure. Journal of Applied Mechanics 35(1): 123–128.

17.

Mignolet

Song

Wang

(2015) A stochastic Iwan-type model for joint behavior variability modeling. Journal of Sound and Vibration 349: 289–298.

18.

Miller

Dane Quinn

(2009) A two-sided interface model for dissipation in structural systems with frictional joints. Journal of Sound and Vibration 321(1): 201–219.

19.

Oldfield

Ouyang

Mottershead

(2005) Simplified models of bolted joints under harmonic loading. Computers & Structures 84(1): 25–33.

20.

Quinn

Segalman

(2005) Using series-series iwan-type models for understanding joint dynamics. Journal of Applied Mechanics 72(5): 666–673.

21.

Rajaei

Ahmadian

(2014) Development of generalized Iwan model to simulate frictional contacts with variable normal loads. Applied Mathematical Modelling 38(15): 4006–4018.

22.

Resor

Starr

(2008) Influence of Misfit Mechanisms on Jointed Structure Response SAND2007-6443C. Albuquerque, NM: Sandia National Laboratories.

23.

Segalman

(2002) A four-parameter Iwan model for lap-type joints. Journal of Applied Mechanics 72(5): 752–760.

24.

Segalman

Star

(2008) Inversion of masing models via continuous Iwan systems. International Journal of Non-Linear Mechanics 43(1): 74–80.

25.

Song

Hartwigsen

Mcfarland

, et al. (2004) Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements. Journal of Sound and Vibration 273(1): 249–276.

26.

Ungar

(1973) The status of engineering knowledge concerning the damping of built-up structures. Journal of Sound and Vibration 26(1): 141–154.

27.

Wang

, et al. (2018) Nonlinear mechanics modeling for joint interface of assembled structure. Chinese Journal of Theoretical and Applied Mechanics 50(1): 44–57.

28.

Xiao

Shao

(2014) Investigation into the energy dissipation of a lap joint using the one-dimensional microslip friction model. European Journal of Mechanics - A/Solids 43: 1–8.

29.

Zhou

Liu

, et al. (2020) The investigation of viscoelastic mechanical behaviors of bolted GLARE joints: modeling and experiments. International Journal of Mechanical Sciences 175: 105538.

30.

Zhang

Xiao

Xie

, et al. (2019) Effects of contact between rough surfaces on the dynamic responses of bolted composite joints: multiscale modeling and numerical simulation. Composite Structures 211: 13–23.