Analytical Solution of Deformations for Two-Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first-order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler-Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variation of stresses and deformations of the beam with the time, compared with those ignoring the memory effect of strains. Finally, the effects of the geometric parameters and material properties of the interlayer on stresses and deformations of the beam are studied in detail.