Free vibration analysis of perforated plate using isogeometric analysis

In this paper, Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is developed to study the free vibration analysis of the perforated plates with different open hole shapes and hole patterns. In this way, the governing equilibrium equations of perforated plate and strain-displacement relations are obtained using the first-order shear-deformable plate theory. The optimal number of control points and the order of the NURBS basis functions are determined to perform physical geometry related to perforated plate geometry. The eigenvalue equations with linear stiffness are established using the weak form of motion equations, energy method and Hamilton principle. The vibrational frequencies and corresponding mode shapes of the perforated plate is derived from governing eigenvalue equations. The results of linear vibrations of plate with central hole are validated considering the previously reported data and finite element analysis, which showed a good agreement. Thereafter, the influence of hole size and shape are explored on the linear vibrations of the plate with hole in same hole area ratio. Further, the effect of the triangular and rectangular pattern under the fully clamped and simply boundary conditions is presented.