High order gradient smoothing towards improved C¹ eigenvalues

Abstract

This article deals with improvement of eigenvalues obtained by finite element analysis of C¹ eigenproblems. The proposed method employs high order gradient smoothing at nodal points to derive improved high order interpolation functions for the single element of each mode. Two different schemes were developed for 1–D C¹ eigenproblems (free vibration of beams) and for 2–D quasi C¹ eigenproblems (transverse vibrations of thin plates). High order Hermitian polynomials are used for the beam problem together with some boundary node corrections, while a combination of high‐order and low‐order approximations are used for the modified formulation of the plate problem. Several smoothing options are proposed for both schemes. Numerical results for both schemes are used as examples to demonstrate the accuracy of the present approach.

Citation

Avrashi, J. (1995), "High order gradient smoothing towards improved C¹ eigenvalues", Engineering Computations, Vol. 12 No. 6, pp. 513-528. https://doi.org/10.1108/02644409510799749