Forced vibration of a bi-axially pre-stressed plate subjected to a harmonic point force and resting on a rigid foundation

This paper models the harmonically forced vibration of a bi-axially pre-stressed plate resting on a rigid foundation using the three-dimensional linearized theory of elastic waves in initially stressed bodies. This model assumes that the material is linearly elastic, homogenous, and isotropic. The model of this system is numerically evaluated using the finite element method simulations. The numerical results illustrate the influence of several system parameters on the dynamic responses of the stresses acting at the interface between the plate and its rigid foundation. The simulations show that the aspect ratio of the plate determines how the initial stress influences the behavior of the system.