NUMERICAL EXPERIMENTS ON RAYLEIGH OPTIMIZATION METHOD WHEN APPLIED TO BEAM VIBRATIONS STUDIED BY MEANS OF THE FINITE-ELEMENT METHOD

Lord Rayleigh suggested in 1894 the use of trial functions containing an undetermined exponential parameter gamma which allows for the optimization of the eigenvalue under study by minimizing it with respect to gamma . In the last five years several authors have, basically, used Lord Rayleigh's optimization concept to solve a variety of problems of elastic stability, vibrations, heat conduction, etc. , and more recently, implemented the methodology in finite elements formulations. Numerical results are presented corresponding to computational experiments performed by the authors in the case of vibrating beams and frames and showing that no computational economy and/or advantage is acquired by using trial functions which contain an unknown parameter when implementing the methodology in a finite element formulation, at least when using the classical Bernouilli theory of vibrating beams.