LAUSR

In this paper, the flexural vibration frequency in the antisymmetric mode of a thick plate as a function of the amplitude of the vibration and the axial force applied is investigated. With this aim, the theory of geometrically nonlinear deformation of second order and an optimized three-dimensional Ritz method are used. The plate is homogeneous, elastically linear, free from any constraints, and subjected to axial forces uniformly distributed on two of its opposite sides. Several approaches are discussed. First, the problem based on finite stress and infinitesimal strains is solved. Second, the deformation energy is assumed as the energy in the initial state plus the vibration energy of small or large amplitude. Third, without assumptions about the size of the deformation and of the vibration amplitude, the theory of nonlinear deformation is employed. Finally, numerical calculations for free vibration are compared with experimental results, including their systematic uncertainties.