Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints

Abstract

Adhesively bonded joints have widely been used in a number of engineering applications, owing to their improved mechanical performance as compared with other mechanical joining techniques, such as rivets or bolts. In this study, a theoretical solution of double-lap joints is established, with functionally graded adhesive and isotopic adherends, under harmonic loads. Assuming a parabolic distribution of the adhesive shear modulus along the overlap length, the analytical harmonic solution is expressed in terms of the solution of the nonlinear Heun differential equation. Furthermore, a two-dimensional finite-element model was developed to validate the analytical solution. We show that using softer adhesive at the edges of the bond line leads to less stress concentration. We also conclude that the adhesive’s shear modulus gradient along the bond line should be greater as the ratio of the adhesive’s shear stiffness to the adherends’ shear stiffness increases. An equation has also been established to determine the optimal shear modulus gradient in terms of the stiffness ratio.