VIBRATION ANALYSIS OF KIRCHOFF’S PLATE USING ISOGEOMETRIC ANALYSIS

Abstract

Vibration analysis of a structure is very important. It can be under the influence of no external force which is known as free vibration, or it can be under the influence of constant force acting on the body which is called as forced vibration. Vibration analysis can be done by using the methods of finite element analysis. Iso-geometric analysis (IGA) is an advanced computing technique in the field of numerical methods. It reduces the computational time as lesser number of elements are required and the analysis is done by using such functions which represent the exact geometry. NURBS functions are used as compared to Lagrangian functions used in FEM. There are many theories for analysis of plates. Kirchhoff’s plate theory is a classical theory used in the analysis of thin plates. The thin plate has many applications in the field of acoustic instruments, electronics industry, aircraft wings. The modal analysis and the consequent mode shape study of the thin plates is very important for their use. Iso-geometric analysis method has been found to be quite effective for the vibration analysis and thus we apply the same to the vibration analysis of thin plate. In order to check the accuracy of IGA results, vibration problems of fixed bar and fixed beam have been studied using IGA. Free vibration analysis of Kirchhoff plate of uniform thickness is done and the IGA model is validated with the exact solution. Based on this model, vibration study of thin isotropic plate with varying thickness is done taking into account four types of variation in profile. This study of varying thickness profiles is the new work that has been done in this study. Linear profile as well as parabolic profiles have been taken both in the decreasing and the increasing form. The variation in the dimensionless frequency number is noted for all the cases in the simply supported case as well as in the fully clamped state. The results obtained are in excellent agreement with the analytical solution and are more accurate than the results obtained by finite element method (FEM). It is found that the plate with variable thickness is stiffer at the edges which are clamped, which in turn increases the natural frequency but it keeps on decreasing as we move along the direction of decreasing thickness.