Geometrically nonlinear rectangular simply supported plates subjected to a moving mass

The dynamic deformation of a geometrically nonlinear rectangular simply supported plate under a moving lumped mass is evaluated using mode expansion method. The governing differential equations of motion for a largely deformable rectangular plate are derived using Lagrange method based on appropriate in and out-of-plane spatial functions which satisfy the proposed boundary conditions. Although the proposed procedure is applicable for any arbitrary edge boundary conditions, only the simply supported plates are addressed in the present work. On the other hand, all inertial components of the moving mass are included in the derivation of the equations of motion. A numerical example is used to study the dynamic behavior of the plate, considering large deformations. The obtained results indicate that ignoring the geometric nonlinearity in determining the vertical deformations of plates under the effect of moving masses, especially those of considerable weight and velocity, results in excessively large linear amplitudes leading to an unfavorable conservative structural design.