COMPARISON OF SIMPLE AND CHEBYSHEV POLYNOMIALS IN RAYLEIGH-RITZ ANALYSIS

The purpose of this paper is to demonstrate the efficacy of using Cheb ychev polynomials in the Rayleigh-Ritz method. For purposes of illustr ation. the problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section of constant cross section subjected to an axial compressive static load and resting on a continu ous elastic foundation is considered. Both simple polynomials as well as orthogonal functions are used as displacement functions in order to demonstrate the advantages of the latter over the former. Two sets of boundary conditions are treated: (1) Fixed-fixed; and (2) fixed-simpl y supported. Wherever possible, the functions are chosen so that the k inematic boundary conditions are satisfied. In the cases in which the functions do not satisfy all the kinematic boundary conditions, the pe nalty-type approach is adopted. In this approach, appropriate springs with large stiffness coefficients are provided to simulate the kinemat ic boundary conditions. Numerical results for natural frequencies and buckling loads for various values of warping and elastic foundation pa rameters are obtained and compared with those obtained by other resear chers. A good agreement is observed.