Vibrations of bonded beams with a single lap adhesive joint

The natural frequencies and loss factors of the coupled longitudinal and flexural vibrations of a system consisting of a pair of parallel and identical elastic cantilevers which are lap-jointed by viscoelastic material over a length a_c from their free ends have been investigated. A complete set of equations of motion and boundary conditions governing the vibration of the system are derived. The solution of these equations, subject to satisfying the boundary conditions, yields the desired natural frequencies and associated composite loss factors. The numerical results have been compared with those from two other approximate methods.