NATURE OF STATIONARITY OF THE NATURAL FREQUENCIES AT THE NATURAL-MODES IN THE RAYLEIGH-RITZ METHOD

A variational formulation of the Rayleigh-Ritz method to obtain approx imate natural frequencies and natural modes is presented. The stationa rity of the natural frequencies with respect to the arbitrary coeffici ents in the linear combination of the assumed deflection shapes, and a lso at the natural modes is investigated. It is concluded that the nat ural frequencies are stationary and need not always be minimum, with r espect to the arbitrary coefficients; however, they are minimum with r espect to the natural modes. This may provide a means of checking the accuracy of the computed natural frequencies obtained by using energy techniques such as the Rayleigh-Ritz, Galerkin, and finite element met hods. (C) 1997 Academic Press Limited.