Dynamic response of assembled structures is strongly dependent on the mechanical behavior of joint interfaces. However, the effect of mechanical joints on structural dynamics is not yet fully understood due to the complex multi-scale, multi-physics and nonlinear characteristics of frictional contact interfaces. A monolithic beam without joint interfaces and a jointed beam with a typical shear lap joint are fabricated. Both structures are subjected to hammer impact excitation to identify the nonlinear effect of joint interfaces. The time-domain responses of both structures are first compared directly to identify the effect of joints. Experimental modal analysis is further used to yield mode shape, frequency and modal damping. The effects of joint interfaces on structural modal properties are investigated. Finally, the wavelet transform analysis and empirical mode decomposition are used to analyze recorded time-domain signals to quantify the effect of joint interfaces on dynamic behavior in time-frequency domain. The results show that joint interfaces play a critical role in dynamic response of assembled structure. The effective stiffness and damping of the lap joint bolt are amplitude dependent. Nonlinear effect of joints on dynamical response is obvious in high-frequency

Wang Dong

Xu Chao

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 107 
Experimental investigation of nonlinear interface effects 
in a jointed beam 
Xu Chao1, Wang Dong2 
School of Astronautics, Northwestern Polytechnical University, Xi’an, 710072, China 
1Corresponding author 
E-mail: 1chao_xu@nwpu.edu.cn, 2king_east@sina.cn 
(Accepted 1 August 2014) 
Abstract. Dynamic response of assembled structures is strongly dependent on the mechanical 
behavior of joint interfaces. However, the effect of mechanical joints on structural dynamics is 
not yet fully understood due to the complex multi-scale, multi-physics and nonlinear 
characteristics of frictional contact interfaces. A monolithic beam without joint interfaces and a 
jointed beam with a typical shear lap joint are fabricated. Both structures are subjected to hammer 
impact excitation to identify the nonlinear effect of joint interfaces. The time-domain responses 
of both structures are first compared directly to identify the effect of joints. Experimental modal 
analysis is further used to yield mode shape, frequency and modal damping. The effects of joint 
interfaces on structural modal properties are investigated. Finally, the wavelet transform analysis 
and empirical mode decomposition are used to analyze recorded time-domain signals to quantify 
the effect of joint interfaces on dynamic behavior in time-frequency domain. The results show that 
joint interfaces play a critical role in dynamic response of assembled structure. The effective 
stiffness and damping of the lap joint bolt are amplitude dependent. Nonlinear effect of joints on 
dynamical response is obvious in high-frequency. 
Keywords: jointed beam, interfaces, nonlinear effect, experimental modal analysis, hammer 
impact test. 
1. Introduction 
Joint interfaces have a significant effect on dynamic response of assembled structures. They 
are considered as the major resource of energy dissipation and stiffness nonlinearity of complex 
structures [1, 2]. Identification and nonlinear modeling of joint interfaces is critical for simulation 
and prediction of dynamic behavior of these structures.  
A number of experimental and theoretical investigations have been carried out to identify the 
nonlinear effect of joint interfaces [3-5]. Beards et al. [6] performed a series of experiments to 
characterize the joint damping. It is found that joint damping is much larger than material  
damping. Gaul et al. [1] carried out the dynamic experiments of a bolted structure, where a 
single-lap joint was located between two large masses. The results reveal hysteresis loop and 
nonlinear softening behavior between the tangential interfaces restoring force and relative 
displacement. Ma et al. [7] investigated the dynamic behavior of a jointed beam and a monolithic 
beam with identical geometry. It is shown that non-proportional damping and nonlinear softening 
stiffness are observed by the presence of joint interfaces. The similar procedure was used by 
Hartwigsen et al [5] to study the nonlinear effect of joint interfaces on the dynamics of a 
lap-jointed beam with a large great mass on each end. However, to characterize the effect of joint 
interfaces on the dynamic properties of a complex structure is still an open problem. 
In this paper, a double-lap jointed beam and a monolithic beam with the identical geometry 
but without joint interfaces are subjected to a series of hammer impact tests. Several dynamic 
analysis methods are applied to analyze the recorded acceleration response. Time-domain 
response and FFT frequency-domain response of both structures are compared to identify the 
effect of joint interfaces. Experimental modal analysis method is used to pull out modal frequency 
and modal damping ratio. The identified modal parameters are compared. Finally, the recorded 
acceleration time-histories are analyzed by two time-frequency signal analysis methods, named 
wavelet transform analysis and empirical mode decomposition (EMD). Multi-scale nonlinear 
EXPERIMENTAL INVESTIGATION OF NONLINEAR INTERFACE EFFECTS IN A JOINTED BEAM.  
XU CHAO, WANG DONG 
108 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
behavior induced by joint interfaces is characterized by these two time-frequency methods. 
2. Experimental beam configurations 
A jointed beam and a monolithic beam with identical geometry were fabricated. The geometry 
dimensions are shown in Fig. 1. Both beams are made of a low-carbon steel, consistent of a 
508×25×8 mm3 simple beam with (jointed beam) or without (monolithic beam) a shear lap joint 
(88×25×8 mm3) in the central section. 
An approximate free-free boundary condition was simulated by suspending the beam at their 
ends from the ceiling. The input excitations applied by model hammer were measured by the 
integral transducer at point A, and response accelerations on each beam were measured by 
miniature single-axial accelerometers attached at point B. All measured data was collected with a 
NI data acquisition cards and inputted to a PC to analyze the data.  
 
Fig. 1. The geometry of the experimental beam 
3. Time-domain response analysis 
Fig. 2 shows the recorded acceleration response histories of the monolithic (left) and the 
jointed beam (right). It can be seen that the acceleration response of the jointed beam decays faster 
than the monolithic beam. Thus, a larger effective damping ratio can be expected for the jointed 
beam. 
 
Fig. 2. Acceleration response time histories of the monolithic and jointed beam 
The FFT amplitude curves of both acceleration signals are illustrated in Fig. 3. It can be seen 
that at the low-frequency interval, both curves are similar, while for the high frequency interval, 
the differences are obvious. The peak frequencies of the jointed beam shift and are lower than the 
peak frequencies of the monolithic beam in high frequency modals. The peak amplitude of the 
jointed beam is smaller than the monolithic beam, which indicates larger damping ability. It is 
noted that for the third modal, the peak nearly disappears for the jointed beam. 
2×Φ10 2×Φ10
A B
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EXPERIMENTAL INVESTIGATION OF NONLINEAR INTERFACE EFFECTS IN A JOINTED BEAM.  
XU CHAO, WANG DONG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 109 
 
Fig. 3. FFT response amplitude of the jointed beam and the monolithic beam 
4. Experimental modal analysis 
Experimental modal analysis was used to extract the modal frequencies and modal damping 
ratio. The experiment schematic diagram is shown in Fig. 4 and the results are listed in Table 1. 
 
Fig. 4. The profile of modal analysis testing 
Table 1. Modal analysis for frequency and damping  
Mode Frequency (Hz) Damping ratios Monolithic Jointed Monolithic Jointed 
1 186.31 174.18 0.0004 0.0017 
2 444.37 433.02 0.0027 0.0026 
3 1013.08 952.43 0.0041 0.0090 
4 1422.85 1353.73 0.0003 0.0035 
5 2609.60 2454.44 0.0007 0.0077 
It can be seen that the normal mode frequencies all decrease for the jointed beam compared 
with the monolithic beam. It turns out that the stiffness of the jointed beam is much lower than the 
monolithic beam due to the presence of the joint interfaces. The damping ratio of each mode of 
the jointed beam is much higher than the monolithic beam except for the second one. The reason 
may be that the node line of the second mode shape is located at the center of the beam. 
Displacement and velocity are nearly constant at the node line during a vibration cycle. Thus, the 
relative interfaces motion and resulted energy dissipation are both unobvious.  
5. Wavelet transform and EMD 
Time domain analysis and frequency analysis cannot give the insight of the system dynamic 
behavior in the time-frequency domain, while time-frequency analysis can give the multi-scale 
information of the system response. Wavelet transform and empirical mode decomposition are 
used here to perform the time-frequency analysis. 
NI data collector
force sensor
accleration sensor
A
LMS modal analysis
monolithic
jointed
B1 B2 B3 B4 B5 B6
contact interfaces
EXPERIMENTAL INVESTIGATION OF NONLINEAR INTERFACE EFFECTS IN A JOINTED BEAM.  
XU CHAO, WANG DONG 
110 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
In mathematics, the wavelet series is a representation of a square-integrable (real- or 
complex-valued) orthonormal function. Nowadays, wavelet transformation is one of the most 
popular candidates of time-frequency-transformations. 
The Hilbert-Huang transform (HHT) is designed to work well for data that is non-stationary 
and nonlinear [8, 9]. The core procedure of HHT is EMD [10]. The EMD method is a necessary 
step to reduce a given data into a collection of intrinsic mode functions (IMFs). Then the Hilbert 
spectral analysis can be applied to obtain instantaneous frequency data. An IMF is defined as a 
function that satisfies the following requirements: 
1) In the whole data set, the number of extreme and the number of zero-crossings must either 
be equal or differ at most by one. 
2) At any point, the mean value of the envelope defined by the local maxima and the envelope 
defined by the local minima is zero. 
The IMFs can be calculated by the following procedure. Given that the time domain signal, 
ݔ(ݐ),  contains ܰ  distinct components at the dominant frequency ߱௠,  resulting in the 
decomposition: 
ݔ(ݐ) = ෍ ܿ௜(ݐ) + ݎ(ݐ),
ே
௜ୀଵ
(1)
where, ݎ(ݐ) is the residual function and ܿ௜(ݐ) indicates the component associated with IMFs. The 
application of EMD yields IMFs sequentially from higher to lower frequency components. The 
main steps of the algorithm for extracting the IMFs of a signal ݔ(ݐ), is summarized as follows: 
1) find all peaks of ݔ(ݐ); 2) perform (spline-) interpolations between minima (maxima), resulting 
in an envelope ݁௠௜௡ and ݁௠௔௫; 3) compute the average ݎ(ݐ) = ( ݁௠௜௡ + ݁௠௔௫)/2; 4) extract the 
residual detail ܿ(ݐ) = ݔ(ݐ) − ݎ(ݐ); and 5) iterate on the residual ݎ(ݐ) (inner loop that iterates) 
until the average ݎ(ݐ) can be considered zero-mean under some tolerance or monotonous series.  
 
Fig. 4. Wavelet transform of time domain response 
Fig. 4 shows the results of wavelet transform of the acceleration time domain response for the 
monolithic beam (left) ant the jointed beam (right). It can be seen that the high frequency time 
domain signal decay very fast due to joint damping. The peak frequencies of high frequency mode 
of the jointed beam are lower than the monolithic beam, which correspond to the results from 
experimental mode analysis. The third peak frequency, near 1000 Hz, disappears on the 
time-frequency plot of the jointed beam. 
The amplitude envelopes of extracted IMFs for the monolithic and jointed beam are illustrated 
in Fig. 5. The IMF1 and IMF2 correspond to structural high frequency response component. It can 
be found that both signals decay very fast, which agrees well with the results from wavelet 
transform. Therefore, the joint interface plays a much more important role for structural high 
frequency response than low frequency. Joint damping is critical to control structural high 
EXPERIMENTAL INVESTIGATION OF NONLINEAR INTERFACE EFFECTS IN A JOINTED BEAM.  
XU CHAO, WANG DONG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 111 
frequency vibration. 
Fig. 5. The IMFs for impact excitation 
Fig. 6 shows the wavelet transform results of each extracted IMF. It can be seen that the central 
frequency of each IMF is corresponded to the modal frequency. The high frequency components 
decay very faster and after a short time, they disappear nearly. It is noted that for nonlinear 
identification of jointed structures, we must make full use of the short time interval high frequency 
response information to yield good identification results. 
 
 
Fig. 6. The wavelet analysis of each IMF 
6. Conclusion 
The aim of the paper is to investigate the effect of joint interfaces on structural dynamic 
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EXPERIMENTAL INVESTIGATION OF NONLINEAR INTERFACE EFFECTS IN A JOINTED BEAM.  
XU CHAO, WANG DONG 
112 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
behavior. Two experimental beams with identical geometry dimensions, one is a monolithic beam 
and the other is a jointed beam with mechanical joint interfaces. Both are subjected to hammer 
impact tests. Several dynamic signal analysis methods, including time-domain analysis, 
experimental mode analysis, wavelet transform, and EMD are used to give insights of the effect 
of joint interfaces on structural dynamic properties.  
Compared with the monolithic beam, the stiffness of the jointed beam decrease and the 
damping increase due to the presence of the joint interfaces. The interfaces effect on structural 
dynamic response mainly is shown in the interval of high frequency. The decaying of high 
frequency component is very fast due to joint damping. It is important to build a nonlinear 
identification method, which can make full use of the response information of high frequency 
component and multi-scale characteristics. The further work will focus on the nonlinear model 
identification of jointed structures. 
Acknowledgment 
It is acknowledged that the present work is supported by the National Science Foundation of 
China through Grants No. 11372246. 
References 
[1] Gaul L., Lenz J. Nonlinear dynamics of structures assembled by bolted joints. Acta Mechanica, 
Vol. 125, 1997, p. 169-181. 
[2] Segalman D. J., Gregory D. L., Starr M. J., Resor B. R., Jew M. D., Lauffer J. P., Ames N. M. 
Handbook on dynamics of jointed structures. Sandia National Laboratories, Albuquerque, 2009. 
[3] Song Y., Hartwigsen C., McFarland D., Vakakis A. F., Bergman L. Simulation of dynamics of 
beam structures with bolted joints using adjusted Iwan beam elements. Journal of Sound and Vibration, 
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[4] Smallwood D. O., Gregory D. L., Coleman R. G. Damping investigations of a simplified frictional 
shear joint. Sandia National Laboratories, Albuquerque, 2000. 
[5] Hartwigsen C. J., Song Y., McFarland D. M., Bergman L., Vakakis A. F. Experimental study of 
non-linear effects in a typical shear lap joint configuration. Journal of Sound and Vibration, Vol. 277, 
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[6] Beards C. F. The damping of structural vibration by controlled interfacial slip in joints. Journal of 
Vibration and Acoustics, Vol. 105, 1983, p. 369-373. 
[7] Ma X., Bergman L., Vakakis A. Identification of bolted joints through laser vibrometry. Journal of 
Sound and Vibration, Vol. 24, 2001, p. 441-460. 
[8] Huang N. E., Shen S. S. Hilbert-Huang Transform and Its Applications. World Scientific, 2005. 
[9] Huang N. E., Wu M. L., Qu W., Long S. R., Shen S. S. Applications of Hilbert-Huang transform to 
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Experimental investigation of nonlinear interface effects in a jointed beam

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Experimental investigation of nonlinear interface effects in a jointed beam

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