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Mechanicalstructures consist of elements that are connected through some types of joints.Bolt joints are commonly used when joining two or more components together inmechanical structures due to its easiness to be assembled and disassembled formaintenance. However, stress cracking due to fatigue, self-loosening, shakingapart, slippage, and breaking due to corrosion is frequentlyfound in bolted joint failures. After fatigue, self-loosening is the mostfrequent cause of failure of dynamically loaded bolted connections.Additionally, fatigue is often initiated by partial loosening 1. Despite theimportance of self-loosening in bolted connections, complete physical andmathematical models in explaining the bolt joint phenomena do not currentlyexist in the literature. Therefore, bolt loosening analysis and detection havebecome an important research area in mechanical engineering in efforts toprevent failures in a variety of mechanical applications.Several methods of bolt modeling have been studied bysome researchers.

For instance, Ibrahim overviewed some dynamical phenomena andcharacteristic of bolted joint, including linear and nonlinear analysis 2.Ahmadian proposed a non-linear generic element formulation for modeling boltedlap joints 3. Bograd overviewed some approaches in modeling the dynamics ofmechanical joints in assembled structures using the finite element method basedon three different approaches: node-to-node contact using the Jenkinsfrictional model, thin layer elements, and zero thickness elements 4.

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Adelpresented a model for predicting the dynamic behavior of bolted joints inhybrid aluminum/composite structures by identifying the Young’s modulus at thejoint affected region. The proposed finite element model was verified by modalexperimental data 5.Furthermore, the experimental detection of the boltedjoint loosening become an important activity in structural health monitoring toensure the proper function and the safety of structures. Several methods havebeen developed regarding the detection of loosening in bolted joints, likeusing electrical conductivity measurement 6, piezo-ceramics actuator andsensor 7, vision-based detection using the Hough transform and support vectormachines 8, and vibration and acoustic measurement and analysis. Vibration and acoustic-based methods have been acommon method to be developed in condition monitoring of a structure, includingjoint condition. Todd investigated the mode shapes of a simple beam based onvaried bolted clamping force obtained from impact testing 9. Ritdumrongkul used a PZT actuator–sensor in conjunctionwith a numerical model-based methodology to quantitatively detect damage ofbolted joints 7.

The loosening of bolts can be quantitatively identified asthe change in stiffness and damping at the bolted joint, indicating a highpotential of this method in order to quantitatively monitor structural damage. The application of a linear transducer array thatgenerates ultrasonic beam using surface acousticwaves (SAWs) transmitted by array elements was proposed. The bolt jointboundaries reflect SAW and array elements receive the echo signals. Thedifferent tightening levels generated different acoustic intensity image 10.Zhang identified bolt loosening and quantitative estimate of the residualtorque, theoretically and experimentally, using two approaches in a comparativemanner: a wave energy dissipation -based linear acoustic approach and a contactacoustic nonlinearity -based vibro-acoustic modulation method 11. Moreover, a vibration testing to detect the bolted joint looseningsystem based on an impulse response excited by laser ablation, whichoffers the potential to measure high frequency vibration responses on thestructure 12.

This paper proposes a simple way to detectquantitatively the looseness of a bolt joint in a cantilever beam model by multi-inputand single output (SISO) modal impact testing. The purpose is to provide a verysimple model that describes structure condition and characteristics with asingle and double bolted connectivity, and it is not the intent to modelspeci?c local behaviors within the joint. The overall goal is to assess to ?rstorder, whether a vibration based modal analysis may be used to assess jointssubject to simple connectivity (clamping force) loss where the connectivity ismodeled by a simple non-linear stiffness function.

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