Free In-Plane Vibration Analysis of Circular, Annular, and Sector Plates Using Isogeometric Approach

Abstract

The in-plane free vibration of sector, annular, and circular plates is investigated by isogeometric finite element approach on the basis of nonuniform rational B-spline (NURBS) basis functions. Under the current framework, both the displacement field and geometry of the sector, annular, and circular plates are modeled by NURBS basis functions to bridge the gap between the design of geometry and the analysis of variable field. The NURBS basic functions can not only preserve the exact geometry of sector, annular, and circular plates, but also provide higher continuity of basis function and its derivatives. The governing equations can be derived by employing the principle of virtual work and the desired solutions are obtained by using the Arnoldi Method. Several numerical examples of sector, annular, and circular plates are performed, and three refinement schemes (the h-, p-, and k-refinement strategies) are applied to demonstrate the convergence. Then the effectiveness and accuracy of the proposed approach are validated through comparisons with results obtained from the finite element analysis as well as open available literature. On this basis, some new numerical results of frequency parameters with mode shapes are shown and may be used as benchmark results for the vibration investigation in the future. In addition, the effects of sector angles and ratio of inside to outside radii on the in-plane vibration of sector, annular, and circular plates under different boundary conditions are fully demonstrated.