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structures consist of elements that are connected through some types of joints.
Bolt joints are commonly used when joining two or more components together in
mechanical structures due to its easiness to be assembled and disassembled for
maintenance. However, stress cracking due to fatigue, self-loosening, shaking
apart, slippage, and breaking due to corrosion is frequently
found in bolted joint failures. After fatigue, self-loosening is the most
frequent cause of failure of dynamically loaded bolted connections.
Additionally, fatigue is often initiated by partial loosening 1. Despite the
importance of self-loosening in bolted connections, complete physical and
mathematical models in explaining the bolt joint phenomena do not currently
exist in the literature. Therefore, bolt loosening analysis and detection have
become an important research area in mechanical engineering in efforts to
prevent failures in a variety of mechanical applications.

Several methods of bolt modeling have been studied by
some researchers. For instance, Ibrahim overviewed some dynamical phenomena and
characteristic of bolted joint, including linear and nonlinear analysis 2.
Ahmadian proposed a non-linear generic element formulation for modeling bolted
lap joints 3. Bograd overviewed some approaches in modeling the dynamics of
mechanical joints in assembled structures using the finite element method based
on three different approaches: node-to-node contact using the Jenkins
frictional model, thin layer elements, and zero thickness elements 4. Adel
presented a model for predicting the dynamic behavior of bolted joints in
hybrid aluminum/composite structures by identifying the Young’s modulus at the
joint affected region. The proposed finite element model was verified by modal
experimental data 5.

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Furthermore, the experimental detection of the bolted
joint loosening become an important activity in structural health monitoring to
ensure the proper function and the safety of structures. Several methods have
been developed regarding the detection of loosening in bolted joints, like
using electrical conductivity measurement 6, piezo-ceramics actuator and
sensor 7, vision-based detection using the Hough transform and support vector
machines 8, and vibration and acoustic measurement and analysis.

Vibration and acoustic-based methods have been a
common method to be developed in condition monitoring of a structure, including
joint condition. Todd investigated the mode shapes of a simple beam based on
varied bolted clamping force obtained from impact testing 9. Ritdumrongkul used a PZT actuator–sensor in conjunction
with a numerical model-based methodology to quantitatively detect damage of
bolted joints 7. The loosening of bolts can be quantitatively identified as
the change in stiffness and damping at the bolted joint, indicating a high
potential of this method in order to quantitatively monitor structural damage.

The application of a linear transducer array that
generates ultrasonic beam using surface acoustic
waves (SAWs) transmitted by array elements was proposed. The bolt joint
boundaries reflect SAW and array elements receive the echo signals. The
different tightening levels generated different acoustic intensity image 10.
Zhang identified bolt loosening and quantitative estimate of the residual
torque, theoretically and experimentally, using two approaches in a comparative
manner: a wave energy dissipation -based linear acoustic approach and a contact
acoustic nonlinearity -based vibro-acoustic modulation method 11. Moreover, a vibration testing to detect the bolted joint loosening
system based on an impulse response excited by laser ablation, which
offers the potential to measure high frequency vibration responses on the
structure 12.

This paper proposes a simple way to detect
quantitatively the looseness of a bolt joint in a cantilever beam model by multi-input
and single output (SISO) modal impact testing. The purpose is to provide a very
simple model that describes structure condition and characteristics with a
single and double bolted connectivity, and it is not the intent to model
speci?c local behaviors within the joint. The overall goal is to assess to ?rst
order, whether a vibration based modal analysis may be used to assess joints
subject to simple connectivity (clamping force) loss where the connectivity is
modeled by a simple non-linear stiffness function.

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