Free vibration analysis of thin plates by using a NURBS-based isogeometric approach

An isogeometric finite element method is presented for natural frequencies analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection field, as for description of the geometry. The governing and discretized equation for the free vibration of the Kirchhoff thin plates is obtained using the standard Galerkin method. Several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of proposed method and compared with the theoretical solutions and other numerical methods.

► The NURBS-based isogeometric method is developed for eigen-value analysis of plates.
► Several numerical simulations of thin plates with various shapes are examined.
► For such eigen-value problems considering various aspect ratios.
► Proposed approach can yield highly accurate solutions of the eigenvalue problems.
► The proposed method is potential and applicable to practical problems of engineering