Influence of adhesive characteristics on the transverse free vibration of single lap-jointed cantilevered beams

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Abstract

This paper deals with the influence of adhesive properties on the transverse free vibration characteristics of single lap-jointed cantilevered beams. The investigations are carried out using the finite element method (FEM). The analysis provides efficient calculations for natural frequencies and mode shapes of the single lap-jointed cantilevered beams, and accounts for various effects of Poisson’s ratio and Young’s modulus of adhesive. Numerical examples are provided to show the influence on the transverse natural frequencies and mode shapes of the single lap-jointed cantilevered beams of different characteristics of adhesives. It is shown that the transverse natural frequencies of single lap-jointed cantilevered beams increase significantly as the Young’s modulus of the adhesive increase, but only slightly change with an increase in Poisson’s ratio. It is also shown that the strength of the adhesive has a very significant effect on the modal properties of the even modes of vibration but an insignificant effect on the modal properties of the odd modes of vibration. The mode shapes show that there are different deformations in the adhesive layer which are not present in a cantilevered beam without a joint. These deformations may cause high stresses in the adhesive layer and may initiate local cracking and delamination failures.

Introduction

There are many industrial applications of structural adhesive joints. These encompass the automotive, aerospace, marine, machine tools and appliance industries. Due to the need to design lightweight structures such as aircraft panels and vehicle body shells, and due to the increased use of lightweight composite materials, there has been a significant increase in use of structural adhesive joints. Structural adhesives are used in place of the traditional mechanical fasteners, such as screws and bolts, because they are much lighter and spread the stresses more uniformly across the joints. The reliability of structural adhesive joint depends on several factors. These factors include the design, materials and manufacturing methods of the joints as well as accurate analysis of the strength of the structural adhesive joints. For efficient designs of adhesively bonded structures, a knowledge of static and dynamic characteristics of adhesive joints is essential. Most theoretical analyses of structural adhesive joints are carried out using analytical equations or finite element method (FEM). Saito and Tani [1], He and Rao [2], [3], Renton and Vinson [4], and Delale and Erdogan [5] have used analytical equations to analyse the static [4], [5] or dynamic [1], [2], [3] properties of adhesive bonded joints. In most of these cases [1], [2], [3], [5], the adherend was homogeneous. However, when the adherend is a composite material, the usual approach is to use the FEM [6], [7], [8], [9]. Ko et al. [6], Reddy [7], Lin and Ko [8] and Yuceoglu et al. [9] have used the FEM to predict the free vibration behaviour of bonded composite plates. Most of these studies concerning free vibration of single lap-jointed beams or plates concentrated on the effects of the overlap ratio, which is the ratio of the overlap length of the joint to the total length of the plate, on the natural frequencies and mode shapes [1], [6].

In this paper, the influence of the characteristics of structural adhesives on the transverse free vibration of single lap-jointed cantilevered beams is investigated theoretically. These investigations are carried out by means of the FEM. Twenty-noded quadratic brick, reduced integration solid elements and 15-noded quadratic triangular prism elements are used to model the single lap-jointed cantilevered beams. The FEM analyses are carried out on a Silicon Graphics Origin 2000 Supercomputer using the commercially available ABAQUS FEA program. Numerical examples are provided to show the influence on the transverse natural frequencies and mode shapes of the single lap-jointed cantilevered beams of the Young’s modulus and Poisson’s ratios of the structural adhesives. From the numerical results, graphical data is produced which will be useful in the design of lap-jointed beam-like structures. The data will enable appropriate choice of the characteristics of the adhesives, especially Young’s modulus, in order to achieve and maintain a satisfactory level of both static and dynamic integrity of the structures.

Section snippets

Configuration and material properties of a single lap-jointed cantilevered beam

The single lap-jointed cantilevered beam studied in this paper includes the lower adherend, adhesive and upper adherend, as shown in Fig. 1. The two adherends used were 2024-T3 aluminium alloy plates of dimensions 200mmlong×50mmwide×4mm thickness. The mechanical properties of the adherends were as follows: Poisson’s ratio, ν=0.33; Young’s modulus, E=70GPa. The mechanical properties of the adhesives investigated were: Poisson’s ratio, νad=0.30, 0.35, 0.40, 0.45 and 0.49999; Young’s modulus, Ead

Finite element modelling

The original finite element mesh is shown in Fig. 2. Most of the adherends and adhesive are modelled using 20-noded quadratic brick, reduced integration solid elements. But at the transition zones from the adherends to the adhesive, where the mesh density is very high, some 15-noded quadratic triangular prism elements are used.

Twenty-noded quadratic brick, reduced integration solid elements belong to second-order isoparametric serendipity elements. The term serendipity refers to the

Results and discussion

For each of the five Poisson’s ratios of the adhesives, results for six natural frequencies, corresponding to various Young’s modulus of adhesive Ead, ranging between 0.001 and 70 GPa are presented in tabular and graphical forms. These are accompanied by selected typical mode shapes.

Conclusions

The influence of adhesive properties on the transverse free vibration characteristics of single lap-jointed beams has been investigated theoretically using the FEM analysis technique. The modal frequencies and mode shapes of transverse free vibration of the beams have been analysed using adhesives of various Young’s modulus and Poisson’s ratio properties. In general, the transverse natural frequencies of the single lap-jointed cantilevered beams increase with an increase in the Young’s modulus

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1

Visiting Scholar from Kunming University of Science and Technology, Kunming, Yunnan Province, PR China.

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