APALAK et al.: OPTIMAL DESIGN OF AN ADHESIVELY BONDED DOUBLE CONTAINMENT CANTILEVER JOINT 797 Journal of Scientific & Industrial Research Vol. 67, October 2008, pp.797-806 *Author for Corresponding Tel: +90 352 437 4901; Fax: +90 352 437 5784 E-mail: apalakmk@erciyes.edu.tr Free vibration analysis and optimal design of an adhesively bonded double containment cantilever joint M Kemal Apalak 1 *, Recep Ekici 1 and Mustafa Yildirim 2 1 Department of Mechanical Engineering, Erciyes University, Kayseri 38039, Turkey 2 Graduate School of Natural and Applied Sciences, Erciyes University, Kayseri 38039, Turkey Received 31 January 2007; revised 21 July 2008; accepted 05 August 2008 This study presents three-dimensional free vibration and stress analyses of an adhesively bonded double containment cantilever joint. Modulus of elasticity, Poisson’s ratio and density had negligible effect on natural frequencies and mode shapes of adhesive joint. ANN models predicted that support length and plate thickness played important role on natural frequencies, mode shapes and modal strain energy of adhesive joint whereas adhesive thickness has a minor effect. Genetic Algorithm combined with ANN model determined optimum geometrical dimensions, which are satisfying maximum natural frequency and minimum elastic modal strain energy conditions for each natural frequency and mode shape of the adhesively bonded double containment cantilever joint. Keywords: ANN, Adhesive joint, Free vibration, Genetic algorithm, Mode shape, Natural frequency, Optimisation Introduction Adhesive bonding technique has been used successfully in joining materials 1-3 . Natural frequencies (NFs) and logarithmic decrement 4 depend on modal number and overlap length. He & Rao 5-6 presented an analytical model to study coupled transverse and longitudinal forced vibration of a simply-supported bonded viscoelastic adhesive lap joint under transverse distributed loads considering both shear and thickness deformation in adhesive layer. Rao & Zhou 7 studied effects of structural parameters and mechanical properties of adhesive layer on system modal loss factors and resonance frequencies for transverse vibration and damping of an adhesively bonded tubular lap joint. Ko et al 8 determined NFs and mode shapes of laminated plates with a lap joint. He & Oyadiji 9 found that mode shapes of lap joint are more pointed for a relatively soft adhesive layer whereas fairly flat for a very stiff adhesive layer. Kaya et al 10 also investigated effects of various parameters on in-plane vibration characteristics of an adhesively bonded single lap joint subjected to two orthogonal in-plane loads. Khalil & Kagho 11 showed that defects caused a reduction in joint stiffness, which leads to a decrease in resonant frequency and an increase in damping capacity. Vaziri & Nayeb- Hashemi 12 investigated effects of tubular joint geometry parameters, material properties and viscoelastic adhesive properties on dynamic response of a tubular adhesive joint subjected to a harmonic axial load and found that system response was sensitive to adhesive loss factor. Yuceoglu et al 13 showed that material characteristics of adhesive layer have significant effect on deformations of bonded multilayer composite plates, their NFs and mode shapes. This study investigates effects of the properties of adhesive layer and geometric dimensions on free vibrations of adhesively bonded double containment cantilever joint. In addition, an optimal design of this adhesive joint is searched based on first 10 NFs and modal strain energies of adhesive joint using artificial neural networks (ANNs) and genetic algorithm. Materials and Methods Joint Configuration and Modal Analysis NFs and mode shapes of an adhesively bonded double containment cantilever joint were investigated (Fig. 1). Support and horizontal plate are made of aluminum and joined with an epoxy adhesive. Support, adhesive layer