On the harmonic response of plates with the shear deformation effect using the elastodynamic solution in the boundary element method

The harmonic response of plates is studied by using the frequency domain solution in conjunction with the direct boundary integral equation (DBIE) for Mindlin's model. The shear deformation and rotatory inertia effects in that model can be switched off in the presented formulation and a DBIE for the classical bending model is then obtained, which includes an additional degree of freedom for the tangential boundary rotation. The frequency responses were obtained to map the plate behavior and they were calculated both with and without the effects of the shear deformation and the rotatory inertia. The analyses were finished when the first natural frequency was identified. The results were compared to available solutions in the literature, employing three-dimensional elasticity theory, the Mindlin and the classical bending models.