The main objective of this paper is to establish the relationship between effective free vibration parameters of an adhesive functionally graded single lap joints and their design variables. This is done by deriving mathematical models which are developed using finite element method (FEM) and design of experiments (DOE) approach. These mathematical models relate the design variables (adhesive thickness, adherends thickness, overlap length and compositional gradient exponent of FGM plates) to the free vibration response parameters (natural frequency and corresponding modal strain energy). In the next stage, to maximize first natural frequency and minimize modal strain energy, simulated annealing (SA) algorithm is used to determine the best design variables. To investigate the performance of proposed procedure, the results of heuristic algorithm are compared with the global optimum obtained by complete enumeration. This comparison shows that the proposed optimization algorithm can efficiently solve such complicated problems. The evaluations of FEM outputs and mathematical models also reveal that the adhesive thickness has a negligible effect on natural frequency and modal strain energy, while other design variables have more significant effects on these design criteria.

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