HIGH-ORDER GRADIENT SMOOTHING TOWARDS IMPROVED C-1 EIGENVALUES

This article deals with improvement of eigenvalues obtained by finite element analysis of C-1 eigenproblems. The proposed method employs hig h order gradient smoothing at nodal points to derive improved high ord er interpolation functions for the single element of each mode. Two di fferent schemes were developed for 1-D C-1 eigenproblems (free vibrati on of beams) and for 2-D quasi C-1 eigenproblems (transverse vibration s of thin plates). High order Hermitian polynomials are used for the b eam problem together with some boundary node corrections, while a comb ination of high-order and low-order approximations are used far the mo dified formulation of the plate problem. Several smoothing options are proposed for both schemes. Numerical results for both schemes are use d as examples to demonstrate the accuracy of the present approach.