Influence of in-plane axial and shear loading on the vibration of metallic plates

This work deals with the vibration problem of metallic plates subjected to combined axial, biaxial and shear in-plane loading. Various type of boundary conditions are considered. Results related to thin plate theories and shear deformation theories are compared to a third-order plate theory including the thickness stretching effects. The Finite Element Method (FEM) is applied on the basis of Carrera Unified Formulation kinematic assumptions. FE matrices are computed by referring to the four-node element. The mixed interpolation of tensorial components technique is used in order to contrast the shear locking for both classical and refined theories. The influence of the in-plane loading (combined axial, biaxial and shear) on plate undamped natural frequencies is illustrated and discussed. Various plate geometries and boundary conditions are considered.