Numerical and experimental investigations of the dynamic response of bonded beams with a single-lap joint

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Abstract

The need to design lightweight structures and the increased use of lightweight materials in industrial fields, have led to wide use of adhesively bonding in recent years. In the design of mechanical systems, which consist of adhesively bonded joints, for minimum vibration response, a specific knowledge of the damping capacity of the component materials and joints is important. It is believed that adhesively bonded joints act to augment the system damping capacity in view of the increasing use of viscoelastic materials in their design. The aim of this paper is to provide an efficient numerical technique for the prediction of the dynamic response of bonded beams with a single-lap joint and to validate the predictions via experimental tests. The finite element method was used to predict the natural frequencies, mode shapes and frequency response functions of the beams. The dynamic test software and the data acquisition hardware were used in the experimental measurement of the dynamic response of the joints. The frequency response functions of the joints of different adherend widths and of different adhesive layer thickness were measured. The frequency response functions and mode shapes predicted using the finite element method were compared with those measured experimentally. The coordination of the numerical and experimental techniques makes it possible to find an efficient tool for studying the dynamic response of bonded beams with a single-lap joint.

Introduction

As a result of the trend towards lightweight construction in manufacturing, there has been a significant increase in the use of adhesively bonded joints in engineering structures and components [1], [2]. In the design of mechanical systems, which consist of adhesively bonded joints, for minimum vibration response, a specific knowledge of the damping capacity of the joints is important. A study into the vibration characteristics of adhesively bonded single lap joints has been carried out by Adams et al. [3] to investigate the effect of joint geometry and temperature variation on overall system damping. Saito and Tani [4] have investigated the natural frequencies and loss factors of coupled longitudinal and flexural vibrations. Miles and Reinhall [5] have presented a comprehensive model for the vibration of a sandwich beam by including the effects of both shear and thickness deformation in the adhesive layer. The equations of motion were derived using Hamilton's principle and solutions were obtained by the Ritz method. Yuceogle et al.'s study [6] was concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The free vibration of bonded single lap joints in composite, shallow circular cylindrical shells or shell panels have also been investigated by Yuceogle and Ozerciyes [7]. To study the flexural vibration of a bonded lap joint system, a theoretical model has been proposed in Rao and Crocker's work [8]. He and Rao [9], [10] established an analytical model to study the coupled transverse and longitudinal vibration of a bonded lap-joint system consisting of a pair of parallel and identical beams which are lap-jointed over a certain length by a viscoelastic material. Vaziri et al. [11] developed a model to study the effects of defects such as a void in the overlap on the system dynamic response. To study the coupled transverse and longitudinal vibrations of a single lap adhesive joint, an analytical model has been described in Ingole and Chatterjee's paper [12].

The increasing complex joint geometry and its three dimensional nature combine to increase the difficulty of obtaining an overall system of governing equations for predicting the dynamic response of adhesively bonded joints. To overcome these problems, the finite element analysis (FEA) is frequently used in the vibration behaviour analysis of bonded beams with a single-lap joint. Rao and Gorrepati's paper [13] presented the analysis of modal parameters of a simply supported beam with adhesively bonded double-strap joint by the FEA based Modal Strain Energy method using the ANSYS 6.4A software. In an early research, the present author and co-worker [14], [15] investigated in detail the influence of the characteristics of structural adhesives on the free transverse and torsional vibration of single-lap cantilevered bonded beams and found that the natural frequencies of the beams increase with increasing adhesive Young's modulus whereas any significant change was not observed with increasing Poisson's ratio. In a research work by Apalak and Yildirim [16], the 3D transient vibration attenuation of an adhesively bonded cantilevered single-lap joint was controlled using actuators. In a similar work by Apalak et al. [17], the response of an adhesively bonded double containment cantilever joint subjected to a transverse excitation force was measured with a contactless eddy-current sensor and the first bending natural frequency was determined using the fast Fourier transform method. In a recent work by Gunes et al. [18], the 3-D free vibration analysis of an adhesively bonded functionally graded tubular single lap joint was carried out using the FEA. The optimal design parameters of the adhesive joint were searched using both the artificial neural networks (ANNs) and the genetic algorithms (GAs).

The aim of this paper is to provide an efficient numerical technique for the prediction of the dynamic response of bonded beams with a single-lap joint and to validate the predictions via experimental tests. The ABAQUS FEA software was used to predict the natural frequencies, mode shapes and frequency response functions (FRFs) of the bonded beams. The LMS (Leuven Measurement System) CADA-X dynamic test software and the LMS-DIFA Scadas II 48 channel data acquisition hardware were used in experimental measurement of the dynamic response of the bonded beams. The FRFs of the bonded beams of different adherend widths and of different adhesive layer thickness were measured. The FRFs and mode shapes predicted using FEA were compared with those measured experimentally. The results show good agreement between the measured and predicted characteristics.

Section snippets

Configuration, material properties and FEA model

Fig. 1 shows the bonded beams with a single-lap joint studied in this work. The two sets of adherends used were aluminium alloy plates of dimensions 200 mm long×25 mm wide×4 mm thickness, and 200 mm long×50 mm wide×4 mm thickness. In order to make it easy to describe the different widths employed, the following nomenclature is used:

  • W25 beam: bonded beam of width 25 mm

  • W50 beam: bonded beam of width 50 mm

The adhesive used was a commercially available two components acryloid cement. The mechanical

Comparison of predicted and measured frequencies of the beams

In this section, the modal properties of the two bonded beams of W25 and W50 predicted using FEA programme and measured using the test rig are compared. The natural frequencies from FEA and from experimental measurement are shown in Table 1, Table 2 and Fig. 4. Although 20 natural frequencies are extracted, the first three natural frequencies are more important. Thus, it can be said that the tables and the figure show good agreements between the measured and predicted natural frequencies of the

Conclusions

With the increase in the use of adhesively bonding in primary structures, such as aircraft and automotive structures, reliable and cost-effective techniques for structural health monitoring (SHM) of adhesive bonding are needed. Vibration-based tests, when combined with validated FEA, can provide a key tool for SHM of adhesive bonding. The dynamic response of the bonded beams with a single-lap joint has been investigated numerically and experimentally in this paper. The ABAQUS FEA software was

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