Longitudinal Vibration and Damping Analysis of Adhesively Bonded Double-Strap Joints

A mathematical model to study the longitudinal vibration of an adhesively bonded double-strap joint is presented in this paper. Energy method and Hamilton’s principle are used to derive the governing equations of motion and natural boundary conditions of the joint system. The adhesive is modeled as a viscoelastic material using complex modulus approach. Both the shear and longitudinal deformation in the adhesive layer are included in the analysis. The equations to predict the system resonance frequencies and loss factors are derived from the system natural and forced boundary conditions for the case of simply supported boundary conditions. A special searching strategy for finding the zeros of a complex determinant has been utilized to obtain the numerical results. The effects of the adhesive shear modulus and structural parameters such as lap ratio, adhesive and strap thickness on the system resonance frequencies and loss factors are also studied.