Abstract
The vibrations and buckling of continuously supported beams resting on elastic foundation impact the design of aircraft structures, highway pavements, and railroad tracks. This article demonstrates the efficacy of Chebychev polynomials in the Rayleigh Ritz method when studying the torsional vibrations and buckling of beams on elastic foundation. Simple polynomials and orthogonal functions serve as displacement functions to illustrate the advantages of orthogonal functions. Fixed-fixed and fixed-simply supported represent the two treated sets of boundary conditions. The functions are chosen so that, most often, the kinematic boundary conditions are satisfied. In some cases, however, a penalty-type approach is used in which appropriate springs with large stiffness coefficients simulate the kinematic boundary conditions. The numerical results for natural frequencies and buckling loads are obtained and compared to the values of other researchers; good agreement is observed.
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