Free vibration analysis of isotropic rectangular plates using a high-order triangular finite element with shear

In this paper, free vibration analysis of isotropic rectangular plates with different thickness ratios, different boundary conditions and different aspect ratios has been investigated using a high-order triangular element. The first-order shear deformation theory (FOSDT) is used to include the effect of transverse shear deformation. The element has 18 nodes on the sides and six internal nodes. The geometry of the element is expressed by three linear shape functions of area coordinates. The formulation is displacement type and the use of area coordinates makes the shape functions for field variables to be expressed explicitly. No numerical integration is required to get the element stiffness and consistent mass matrices. The element has 51 degrees of freedom, which can be reduced to 39 degrees of freedom by Guyan reduction, mass condensation, or eigenvalue economization scheme for the degrees of freedom associated with the internal nodes. Rotary inertia has been included in the consistent mass matrix. Numerical examples are presented to show the accuracy and convergence characteristics of the element.