Abstract
An analytical model to study the coupled transverse and longitudinal vibration of a bonded lap joint system is described in this paper. The system consists of a pair of parallel and identical beams which are lap-jointed over a certain length by a viscoelastic material. The unjointed ends of the beams are assumed to be simply supported. The governing equations of motion for the forced vibration of the system under transverse distributed loads are derived using the energy method and Hamilton's principle. Both shear and thickness deformation in the adhesive layer is included in the analysis. The theoretical development of the model is presented in this paper. The numerical solutions of the governing equations for free vibration along with boundary and continuity conditions yield the system natural frequencies, loss factors and mode shapes. The details of the numerical solution scheme and results for free vibration are included in the accompanying paper.
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