In this paper, free vibration characteristics of an adhesive functionally graded single lap joint are modeled and an optimal design procedure for such structures has been proposed. To establish the relationship between the design variables and effective free vibration parameters, a mathematical model is developed for the analysis of free vibration of an adhesive joint using finite element method (FEM), design of experiment (DOE), and regression analysis. These models relate the design variables (adhesive thickness, adherends thickness, overlap length, and compositional gradient exponent of functionally graded plates) to the effective free vibration parameters (natural frequency and corresponding modal strain energy). To simultaneously maximize the first natural frequency and minimize the modal strain energy, for any given set of design parameters, a simulated annealing (SA) algorithm is applied to the developed models. To investigate the performance of proposed procedure, the results of heuristic algorithm are compared with all possible solutions (complete enumeration). This comparison shows that the proposed solution procedure can effectively 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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